LMFDB - Embedded newform 504.2.be.a.139.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(139,504)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 2, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("504.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.be (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$92$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			139.3
Character	$\chi$	$=$	504.139
Dual form			504.2.be.a.475.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41366 - 0.0394185i) q^{2} +(-1.54504 + 0.782839i) q^{3} +(1.99689 + 0.111449i) q^{4} +(1.11062 - 1.92366i) q^{5} +(2.21503 - 1.04577i) q^{6} +(-2.08899 + 1.62361i) q^{7} +(-2.81854 - 0.236266i) q^{8} +(1.77433 - 2.41904i) q^{9} +O(q^{10})$	\(q+(-1.41366 - 0.0394185i) q^{2} +(-1.54504 + 0.782839i) q^{3} +(1.99689 + 0.111449i) q^{4} +(1.11062 - 1.92366i) q^{5} +(2.21503 - 1.04577i) q^{6} +(-2.08899 + 1.62361i) q^{7} +(-2.81854 - 0.236266i) q^{8} +(1.77433 - 2.41904i) q^{9} +(-1.64588 + 2.67563i) q^{10} +(1.45488 + 2.51993i) q^{11} +(-3.17253 + 1.39105i) q^{12} +(-2.08438 + 3.61026i) q^{13} +(3.01714 - 2.21289i) q^{14} +(-0.210050 + 3.84158i) q^{15} +(3.97516 + 0.445104i) q^{16} -6.76243i q^{17} +(-2.60366 + 3.34977i) q^{18} -3.23484i q^{19} +(2.43219 - 3.71756i) q^{20} +(1.95657 - 4.14389i) q^{21} +(-1.95738 - 3.61968i) q^{22} +(7.20408 + 4.15928i) q^{23} +(4.53973 - 1.84142i) q^{24} +(0.0330268 + 0.0572040i) q^{25} +(3.08893 - 5.02153i) q^{26} +(-0.847693 + 5.12654i) q^{27} +(-4.35245 + 3.00935i) q^{28} +(-2.79971 + 1.61641i) q^{29} +(0.448370 - 5.42242i) q^{30} +(-2.65268 + 4.59457i) q^{31} +(-5.60199 - 0.785922i) q^{32} +(-4.22055 - 2.75446i) q^{33} +(-0.266565 + 9.55981i) q^{34} +(0.803179 + 5.82173i) q^{35} +(3.81274 - 4.63282i) q^{36} +9.29723i q^{37} +(-0.127512 + 4.57297i) q^{38} +(0.394215 - 7.20975i) q^{39} +(-3.58484 + 5.15951i) q^{40} +(10.3483 + 5.97460i) q^{41} +(-2.92927 + 5.78095i) q^{42} +(3.43228 + 5.94488i) q^{43} +(2.62440 + 5.19417i) q^{44} +(-2.68280 - 6.09984i) q^{45} +(-10.0202 - 6.16379i) q^{46} +(-1.08449 - 1.87839i) q^{47} +(-6.49024 + 2.42420i) q^{48} +(1.72779 - 6.78342i) q^{49} +(-0.0444338 - 0.0821691i) q^{50} +(5.29390 + 10.4483i) q^{51} +(-4.56465 + 6.97700i) q^{52} +2.43270i q^{53} +(1.40043 - 7.21379i) q^{54} +6.46330 q^{55} +(6.27152 - 4.08265i) q^{56} +(2.53236 + 4.99797i) q^{57} +(4.02156 - 2.17470i) q^{58} +(-1.17901 - 0.680701i) q^{59} +(-0.847588 + 7.64781i) q^{60} +(4.35247 + 7.53869i) q^{61} +(3.93111 - 6.39062i) q^{62} +(0.221020 + 7.93418i) q^{63} +(7.88836 + 1.33185i) q^{64} +(4.62994 + 8.01928i) q^{65} +(5.85787 + 4.06025i) q^{66} +(-3.35416 + 5.80957i) q^{67} +(0.753668 - 13.5039i) q^{68} +(-14.3867 - 0.786635i) q^{69} +(-0.905941 - 8.26163i) q^{70} -2.98220i q^{71} +(-5.57255 + 6.39896i) q^{72} +3.83642i q^{73} +(0.366483 - 13.1432i) q^{74} +(-0.0958094 - 0.0625281i) q^{75} +(0.360520 - 6.45962i) q^{76} +(-7.13061 - 2.90196i) q^{77} +(-0.841486 + 10.1766i) q^{78} +(8.65919 - 4.99939i) q^{79} +(5.27114 - 7.15250i) q^{80} +(-2.70353 - 8.58434i) q^{81} +(-14.3935 - 8.85399i) q^{82} +(-6.16981 + 3.56214i) q^{83} +(4.36888 - 8.05685i) q^{84} +(-13.0086 - 7.51052i) q^{85} +(-4.61775 - 8.53935i) q^{86} +(3.06028 - 4.68915i) q^{87} +(-3.50527 - 7.44626i) q^{88} +16.7883i q^{89} +(3.55213 + 8.72888i) q^{90} +(-1.50738 - 10.9260i) q^{91} +(13.9222 + 9.10851i) q^{92} +(0.501695 - 9.17544i) q^{93} +(1.45906 + 2.69816i) q^{94} +(-6.22272 - 3.59269i) q^{95} +(9.27058 - 3.17117i) q^{96} +(7.04084 - 4.06503i) q^{97} +(-2.70991 + 9.52136i) q^{98} +(8.67724 + 0.951755i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q - 2 q^{2} - 2 q^{4} - 8 q^{8} - 8 q^{9}+O(q^{10}) $ 184 * q - 2 * q^2 - 2 * q^4 - 8 * q^8 - 8 * q^9	$ 184 q - 2 q^{2} - 2 q^{4} - 8 q^{8} - 8 q^{9} - 4 q^{11} - 10 q^{14} - 2 q^{16} - 10 q^{18} + 6 q^{22} - 80 q^{25} - 12 q^{28} + 4 q^{30} - 12 q^{32} + 12 q^{35} - 46 q^{36} + 10 q^{42} - 4 q^{43} - 36 q^{44} - 16 q^{46} - 2 q^{49} + 16 q^{50} - 24 q^{51} + 40 q^{56} + 16 q^{57} - 10 q^{58} + 40 q^{60} - 8 q^{64} + 36 q^{65} - 4 q^{67} - 76 q^{72} - 40 q^{74} + 60 q^{78} + 8 q^{81} + 40 q^{84} + 32 q^{86} - 18 q^{88} + 20 q^{91} - 26 q^{92} - 132 q^{98} + 28 q^{99}+O(q^{100}) $ 184 * q - 2 * q^2 - 2 * q^4 - 8 * q^8 - 8 * q^9 - 4 * q^11 - 10 * q^14 - 2 * q^16 - 10 * q^18 + 6 * q^22 - 80 * q^25 - 12 * q^28 + 4 * q^30 - 12 * q^32 + 12 * q^35 - 46 * q^36 + 10 * q^42 - 4 * q^43 - 36 * q^44 - 16 * q^46 - 2 * q^49 + 16 * q^50 - 24 * q^51 + 40 * q^56 + 16 * q^57 - 10 * q^58 + 40 * q^60 - 8 * q^64 + 36 * q^65 - 4 * q^67 - 76 * q^72 - 40 * q^74 + 60 * q^78 + 8 * q^81 + 40 * q^84 + 32 * q^86 - 18 * q^88 + 20 * q^91 - 26 * q^92 - 132 * q^98 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.41366	−	0.0394185i	−0.999611	−	0.0278731i
$2$	−1.41366	−	0.0394185i	−0.999611	−	0.0278731i
$3$	−1.54504	+	0.782839i	−0.892032	+	0.451972i
$3$	−1.54504	+	0.782839i	−0.892032	+	0.451972i
$4$	1.99689	+	0.111449i	0.998446	+	0.0557246i
$5$	1.11062	−	1.92366i	0.496686	−	0.860286i	−0.503306	−	0.864108i	$-0.667883\pi$
$5$	1.11062	−	1.92366i	0.496686	−	0.860286i	0.999993	+	0.00382206i	$0.00121660\pi$
$6$	2.21503	−	1.04577i	0.904283	−	0.426933i
$7$	−2.08899	+	1.62361i	−0.789566	+	0.613666i
$7$	−2.08899	+	1.62361i	−0.789566	+	0.613666i
$8$	−2.81854	−	0.236266i	−0.996505	−	0.0835327i
$9$	1.77433	−	2.41904i	0.591442	−	0.806347i
$10$	−1.64588	+	2.67563i	−0.520472	+	0.846108i
$11$	1.45488	+	2.51993i	0.438663	+	0.759787i	0.997587	−	0.0694326i	$-0.0221189\pi$
$11$	1.45488	+	2.51993i	0.438663	+	0.759787i	−0.558924	+	0.829219i	$0.688786\pi$
$12$	−3.17253	+	1.39105i	−0.915832	+	0.401562i
$13$	−2.08438	+	3.61026i	−0.578104	+	1.00131i	0.417593	+	0.908634i	$0.362874\pi$
$13$	−2.08438	+	3.61026i	−0.578104	+	1.00131i	−0.995697	+	0.0926714i	$0.970459\pi$
$14$	3.01714	−	2.21289i	0.806364	−	0.591420i
$15$	−0.210050	+	3.84158i	−0.0542347	+	0.991891i
$16$	3.97516	+	0.445104i	0.993790	+	0.111276i
$17$		−	6.76243i		−	1.64013i	−0.572269	−	0.820066i	$-0.693937\pi$
$17$		−	6.76243i		−	1.64013i	0.572269	−	0.820066i	$-0.306063\pi$
$18$	−2.60366	+	3.34977i	−0.613688	+	0.789549i
$19$		−	3.23484i		−	0.742122i	−0.928608	−	0.371061i	$-0.878994\pi$
$19$		−	3.23484i		−	0.742122i	0.928608	−	0.371061i	$-0.121006\pi$
$20$	2.43219	−	3.71756i	0.543854	−	0.831272i
$21$	1.95657	−	4.14389i	0.426958	−	0.904272i
$22$	−1.95738	−	3.61968i	−0.417315	−	0.771718i
$23$	7.20408	+	4.15928i	1.50215	+	0.867269i	0.999997	+	0.00249254i	$0.000793400\pi$
$23$	7.20408	+	4.15928i	1.50215	+	0.867269i	0.502157	+	0.864776i	$0.332540\pi$
$24$	4.53973	−	1.84142i	0.926669	−	0.375879i
$25$	0.0330268	+	0.0572040i	0.00660535	+	0.0114408i
$26$	3.08893	−	5.02153i	0.605789	−	0.984803i
$27$	−0.847693	+	5.12654i	−0.163139	+	0.986603i
$28$	−4.35245	+	3.00935i	−0.822535	+	0.568715i
$29$	−2.79971	+	1.61641i	−0.519892	+	0.300160i	−0.736891	−	0.676012i	$-0.763707\pi$
$29$	−2.79971	+	1.61641i	−0.519892	+	0.300160i	0.216998	+	0.976172i	$0.430373\pi$
$30$	0.448370	−	5.42242i	0.0818607	−	0.989994i
$31$	−2.65268	+	4.59457i	−0.476435	+	0.825209i	−0.999635	−	0.0270003i	$-0.991405\pi$
$31$	−2.65268	+	4.59457i	−0.476435	+	0.825209i	0.523201	+	0.852210i	$0.324738\pi$
$32$	−5.60199	−	0.785922i	−0.990302	−	0.138933i
$33$	−4.22055	−	2.75446i	−0.734704	−	0.479490i
$34$	−0.266565	+	9.55981i	−0.0457156	+	1.63949i
$35$	0.803179	+	5.82173i	0.135762	+	0.984052i
$36$	3.81274	−	4.63282i	0.635456	−	0.772137i
$37$			9.29723i			1.52846i	0.644947	+	0.764228i	$0.276880\pi$
$37$			9.29723i			1.52846i	−0.644947	+	0.764228i	$0.723120\pi$
$38$	−0.127512	+	4.57297i	−0.0206853	+	0.741834i
$39$	0.394215	−	7.20975i	0.0631249	−	1.15448i
$40$	−3.58484	+	5.15951i	−0.566812	+	0.815790i
$41$	10.3483	+	5.97460i	1.61613	+	0.933075i	0.987907	+	0.155045i	$0.0495523\pi$
$41$	10.3483	+	5.97460i	1.61613	+	0.933075i	0.628227	+	0.778030i	$0.283781\pi$
$42$	−2.92927	+	5.78095i	−0.451997	+	0.892020i
$43$	3.43228	+	5.94488i	0.523417	+	0.906585i	0.999629	+	0.0272544i	$0.00867641\pi$
$43$	3.43228	+	5.94488i	0.523417	+	0.906585i	−0.476211	+	0.879331i	$0.657990\pi$
$44$	2.62440	+	5.19417i	0.395643	+	0.783050i
$45$	−2.68280	−	6.09984i	−0.399928	−	0.909311i
$46$	−10.0202	−	6.16379i	−1.47740	−	0.908802i
$47$	−1.08449	−	1.87839i	−0.158189	−	0.273992i	0.776027	−	0.630700i	$-0.217232\pi$
$47$	−1.08449	−	1.87839i	−0.158189	−	0.273992i	−0.934216	+	0.356709i	$0.883899\pi$
$48$	−6.49024	+	2.42420i	−0.936786	+	0.349904i
$49$	1.72779	−	6.78342i	0.246827	−	0.969059i
$50$	−0.0444338	−	0.0821691i	−0.00628389	−	0.0116205i
$51$	5.29390	+	10.4483i	0.741294	+	1.46305i
$52$	−4.56465	+	6.97700i	−0.633003	+	0.967535i
$53$			2.43270i			0.334157i	0.985944	+	0.167079i	$0.0534333\pi$
$53$			2.43270i			0.334157i	−0.985944	+	0.167079i	$0.946567\pi$
$54$	1.40043	−	7.21379i	0.190575	−	0.981673i
$55$	6.46330			0.871512
$56$	6.27152	−	4.08265i	0.838067	−	0.545567i
$57$	2.53236	+	4.99797i	0.335419	+	0.661997i
$58$	4.02156	−	2.17470i	0.528057	−	0.285552i
$59$	−1.17901	−	0.680701i	−0.153494	−	0.0886197i	0.421286	−	0.906928i	$-0.361579\pi$
$59$	−1.17901	−	0.680701i	−0.153494	−	0.0886197i	−0.574780	+	0.818308i	$0.694912\pi$
$60$	−0.847588	+	7.64781i	−0.109423	+	0.987328i
$61$	4.35247	+	7.53869i	0.557276	+	0.965231i	0.997723	+	0.0674517i	$0.0214868\pi$
$61$	4.35247	+	7.53869i	0.557276	+	0.965231i	−0.440446	+	0.897779i	$0.645180\pi$
$62$	3.93111	−	6.39062i	0.499251	−	0.811609i
$63$	0.221020	+	7.93418i	0.0278459	+	0.999612i
$64$	7.88836	+	1.33185i	0.986045	+	0.166482i
$65$	4.62994	+	8.01928i	0.574273	+	0.994670i
$66$	5.85787	+	4.06025i	0.721053	+	0.499783i
$67$	−3.35416	+	5.80957i	−0.409775	+	0.709752i	−0.994864	−	0.101217i	$-0.967726\pi$
$67$	−3.35416	+	5.80957i	−0.409775	+	0.709752i	0.585089	+	0.810969i	$0.301060\pi$
$68$	0.753668	−	13.5039i	0.0913956	−	1.63758i
$69$	−14.3867	−	0.786635i	−1.73195	−	0.0946997i
$70$	−0.905941	−	8.26163i	−0.108281	−	0.987454i
$71$		−	2.98220i		−	0.353922i	−0.984218	−	0.176961i	$-0.943373\pi$
$71$		−	2.98220i		−	0.353922i	0.984218	−	0.176961i	$-0.0566266\pi$
$72$	−5.57255	+	6.39896i	−0.656731	+	0.754125i
$73$			3.83642i			0.449019i	0.974472	+	0.224510i	$0.0720780\pi$
$73$			3.83642i			0.449019i	−0.974472	+	0.224510i	$0.927922\pi$
$74$	0.366483	−	13.1432i	0.0426028	−	1.52786i
$75$	−0.0958094	−	0.0625281i	−0.0110631	−	0.00722013i
$76$	0.360520	−	6.45962i	0.0413544	−	0.740969i
$77$	−7.13061	−	2.90196i	−0.812608	−	0.330709i
$78$	−0.841486	+	10.1766i	−0.0952795	+	1.15228i
$79$	8.65919	−	4.99939i	0.974235	−	0.562475i	0.0737103	−	0.997280i	$-0.476516\pi$
$79$	8.65919	−	4.99939i	0.974235	−	0.562475i	0.900525	+	0.434805i	$0.143183\pi$
$80$	5.27114	−	7.15250i	0.589331	−	0.799674i
$81$	−2.70353	−	8.58434i	−0.300392	−	0.953816i
$82$	−14.3935	−	8.85399i	−1.58950	−	0.977760i
$83$	−6.16981	+	3.56214i	−0.677225	+	0.390996i	−0.798809	−	0.601585i	$-0.794536\pi$
$83$	−6.16981	+	3.56214i	−0.677225	+	0.390996i	0.121584	+	0.992581i	$0.461203\pi$
$84$	4.36888	−	8.05685i	0.476684	−	0.879075i
$85$	−13.0086	−	7.51052i	−1.41098	−	0.814631i
$86$	−4.61775	−	8.53935i	−0.497945	−	0.920822i
$87$	3.06028	−	4.68915i	0.328097	−	0.502729i
$88$	−3.50527	−	7.44626i	−0.373663	−	0.793774i
$89$			16.7883i			1.77955i	0.456395	+	0.889777i	$0.349140\pi$
$89$			16.7883i			1.77955i	−0.456395	+	0.889777i	$0.650860\pi$
$90$	3.55213	+	8.72888i	0.374427	+	0.920105i
$91$	−1.50738	−	10.9260i	−0.158016	−	1.14536i
$92$	13.9222	+	9.10851i	1.45149	+	0.949628i
$93$	0.501695	−	9.17544i	0.0520234	−	0.951448i
$94$	1.45906	+	2.69816i	0.150491	+	0.278294i
$95$	−6.22272	−	3.59269i	−0.638437	−	0.368602i
$96$	9.27058	−	3.17117i	0.946175	−	0.323656i
$97$	7.04084	−	4.06503i	0.714889	−	0.412741i	−0.0979796	−	0.995188i	$-0.531238\pi$
$97$	7.04084	−	4.06503i	0.714889	−	0.412741i	0.812869	+	0.582447i	$0.197905\pi$
$98$	−2.70991	+	9.52136i	−0.273742	+	0.961803i
$99$	8.67724	+	0.951755i	0.872096	+	0.0956550i
$100$	0.0595755	+	0.117911i	0.00595755	+	0.0117911i
$101$	−3.71422	−	6.43323i	−0.369579	−	0.640130i	0.619921	−	0.784665i	$-0.287165\pi$
$101$	−3.71422	−	6.43323i	−0.369579	−	0.640130i	−0.989500	+	0.144535i	$0.953831\pi$
$102$	−7.07194	−	14.9790i	−0.700226	−	1.48314i
$103$	−0.913758	+	1.58268i	−0.0900353	+	0.155946i	−0.907526	−	0.419996i	$-0.862031\pi$
$103$	−0.913758	+	1.58268i	−0.0900353	+	0.155946i	0.817490	+	0.575942i	$0.195365\pi$
$104$	6.72791	−	9.68320i	0.659726	−	0.949516i
$105$	−5.79842	−	8.36607i	−0.565868	−	0.816445i
$106$	0.0958935	−	3.43902i	0.00931400	−	0.334027i
$107$	−7.09643			−0.686038			−0.343019	−	0.939329i	$-0.611449\pi$
$107$	−7.09643			−0.686038			−0.343019	+	0.939329i	$0.611449\pi$
$108$	−2.26410	+	10.1427i	−0.217863	+	0.975979i
$109$		−	1.46214i		−	0.140048i	−0.997545	−	0.0700240i	$-0.977692\pi$
$109$		−	1.46214i		−	0.140048i	0.997545	−	0.0700240i	$-0.0223076\pi$
$110$	−9.13694	−	0.254774i	−0.871173	−	0.0242917i
$111$	−7.27823	−	14.3646i	−0.690819	−	1.36343i
$112$	−9.02676	+	5.52428i	−0.852948	+	0.521995i
$113$	8.34250	−	14.4496i	0.784796	−	1.35931i	−0.144325	−	0.989530i	$-0.546101\pi$
$113$	8.34250	−	14.4496i	0.784796	−	1.35931i	0.929121	−	0.369776i	$-0.120566\pi$
$114$	−3.38289	−	7.16527i	−0.316836	−	0.671089i
$115$	16.0020	−	9.23879i	1.49220	−	0.861521i
$116$	−5.77086	+	2.91577i	−0.535811	+	0.270723i
$117$	5.03499	+	11.4480i	0.465485	+	1.05837i
$118$	1.63989	+	1.00876i	0.150964	+	0.0928636i
$119$	10.9795	+	14.1267i	1.00649	+	1.29499i
$120$	1.49967	−	10.7780i	0.136901	−	0.983894i
$121$	1.26665	−	2.19390i	0.115150	−	0.199445i
$122$	−5.85576	−	10.8287i	−0.530156	−	0.980389i
$123$	−20.6657	−	1.12996i	−1.86337	−	0.101885i
$124$	−5.80917	+	8.87922i	−0.521679	+	0.797378i
$125$	11.2530			1.00650
$126$	0.000305646	−	11.2250i	2.72291e−5	−	1.00000i
$127$		−	3.89917i		−	0.345995i	−0.984922	−	0.172998i	$-0.944655\pi$
$127$		−	3.89917i		−	0.345995i	0.984922	−	0.172998i	$-0.0553453\pi$
$128$	−11.0990	−	2.19374i	−0.981021	−	0.193901i
$129$	−9.95690	−	6.49818i	−0.876656	−	0.572133i
$130$	−6.22907	−	11.5191i	−0.546325	−	1.01029i
$131$	−6.77481	−	3.91144i	−0.591918	−	0.341744i	0.173937	−	0.984757i	$-0.444351\pi$
$131$	−6.77481	−	3.91144i	−0.591918	−	0.341744i	−0.765856	+	0.643013i	$0.777684\pi$
$132$	−8.12101	−	5.97074i	−0.706843	−	0.519686i
$133$	5.25211	+	6.75755i	0.455415	+	0.585954i
$134$	4.97065	−	8.08056i	0.429399	−	0.698054i
$135$	8.92024	+	7.32433i	0.767732	+	0.630378i
$136$	−1.59774	+	19.0602i	−0.137005	+	1.63440i
$137$	−4.47612	−	7.75286i	−0.382421	−	0.662372i	0.608987	−	0.793180i	$-0.291576\pi$
$137$	−4.47612	−	7.75286i	−0.382421	−	0.662372i	−0.991408	+	0.130808i	$0.958243\pi$
$138$	20.3069	+	1.67914i	1.72864	+	0.142938i
$139$	1.82333	+	1.05270i	0.154653	+	0.0892890i	0.575329	−	0.817922i	$-0.304874\pi$
$139$	1.82333	+	1.05270i	0.154653	+	0.0892890i	−0.420676	+	0.907211i	$0.638207\pi$
$140$	0.955035	+	11.7149i	0.0807152	+	0.990088i
$141$	3.14606	+	2.05322i	0.264946	+	0.172912i
$142$	−0.117554	+	4.21582i	−0.00986490	+	0.353784i
$143$	−12.1301			−1.01437
$144$	8.12995	−	8.82632i	0.677496	−	0.735526i
$145$			7.18090i			0.596341i
$146$	0.151226	−	5.42341i	0.0125156	−	0.448845i
$147$	2.64081	+	11.8333i	0.217810	+	0.975991i
$148$	−1.03617	+	18.5656i	−0.0851725	+	1.52608i
$149$	−5.88766	−	3.39924i	−0.482336	−	0.278477i	0.239054	−	0.971006i	$-0.423163\pi$
$149$	−5.88766	−	3.39924i	−0.482336	−	0.278477i	−0.721389	+	0.692530i	$0.756496\pi$
$150$	0.132977	+	0.0921705i	0.0108576	+	0.00752569i
$151$	−3.59214	+	2.07392i	−0.292324	+	0.168773i	−0.638990	−	0.769215i	$-0.720647\pi$
$151$	−3.59214	+	2.07392i	−0.292324	+	0.168773i	0.346665	+	0.937989i	$0.387314\pi$
$152$	−0.764282	+	9.11752i	−0.0619915	+	0.739528i
$153$	−16.3586	−	11.9988i	−1.32252	−	0.970043i
$154$	9.96590	+	4.38347i	0.803075	+	0.353230i
$155$	5.89225	+	10.2057i	0.473277	+	0.819740i
$156$	1.59073	−	14.3532i	0.127360	−	1.14917i
$157$	2.87614	−	4.98162i	0.229541	−	0.397577i	−0.728131	−	0.685438i	$-0.759611\pi$
$157$	2.87614	−	4.98162i	0.229541	−	0.397577i	0.957672	+	0.287861i	$0.0929441\pi$
$158$	−12.4383	+	6.72612i	−0.989534	+	0.535101i
$159$	−1.90441	−	3.75863i	−0.151030	−	0.298079i
$160$	−7.73356	+	9.90345i	−0.611391	+	0.782937i
$161$	−21.8023	+	3.00790i	−1.71826	+	0.237055i
$162$	3.48350	+	12.2419i	0.273690	+	0.961818i
$163$	12.6277			0.989078			0.494539	−	0.869156i	$-0.335337\pi$
$163$	12.6277			0.989078			0.494539	+	0.869156i	$0.335337\pi$
$164$	19.9986	+	13.0839i	1.56163	+	1.02168i
$165$	−9.98609	+	5.05973i	−0.777416	+	0.393899i
$166$	8.86245	−	4.79247i	0.687860	−	0.371968i
$167$	−3.69127	+	6.39346i	−0.285639	+	0.494741i	−0.972764	−	0.231798i	$-0.925539\pi$
$167$	−3.69127	+	6.39346i	−0.285639	+	0.494741i	0.687125	+	0.726539i	$0.258872\pi$
$168$	−6.49372	+	11.2175i	−0.501002	+	0.865446i
$169$	−2.18932	−	3.79201i	−0.168409	−	0.291693i
$170$	18.0938	+	11.1301i	1.38773	+	0.853643i
$171$	−7.82520	−	5.73965i	−0.598408	−	0.438922i
$172$	6.19134	+	12.2538i	0.472085	+	0.934344i
$173$	−3.23659	−	5.60594i	−0.246073	−	0.426211i	0.716360	−	0.697731i	$-0.245807\pi$
$173$	−3.23659	−	5.60594i	−0.246073	−	0.426211i	−0.962433	+	0.271520i	$0.912474\pi$
$174$	−4.51105	+	6.50824i	−0.341982	+	0.493389i
$175$	−0.161870	−	0.0658764i	−0.0122362	−	0.00497978i
$176$	4.66175	+	10.6647i	0.351393	+	0.803881i
$177$	2.35450	+	0.128739i	0.176975	+	0.00967665i
$178$	0.661770	−	23.7330i	0.0496017	−	1.77886i
$179$	−6.58449			−0.492148			−0.246074	−	0.969251i	$-0.579141\pi$
$179$	−6.58449			−0.492148			−0.246074	+	0.969251i	$0.579141\pi$
$180$	−4.67744	−	12.4797i	−0.348636	−	0.930184i
$181$	21.4157			1.59181			0.795907	−	0.605419i	$-0.206994\pi$
$181$	21.4157			1.59181			0.795907	+	0.605419i	$0.206994\pi$
$182$	1.70024	+	15.5052i	0.126030	+	1.14932i
$183$	−12.6263	−	8.24034i	−0.933366	−	0.609143i
$184$	−19.3223	−	13.4252i	−1.42446	−	0.989717i
$185$	17.8847	+	10.3257i	1.31491	+	0.759163i
$186$	−1.07091	+	12.9512i	−0.0785230	+	0.949629i
$187$	17.0408	−	9.83853i	1.24615	−	0.719465i
$188$	−1.95626	−	3.87181i	−0.142675	−	0.282381i
$189$	−6.55267	−	12.0856i	−0.476636	−	0.879101i
$190$	8.65521	+	5.32414i	0.627915	+	0.386254i
$191$	−3.59920	+	2.07800i	−0.260429	+	0.150359i	−0.624530	−	0.781001i	$-0.714709\pi$
$191$	−3.59920	+	2.07800i	−0.260429	+	0.150359i	0.364101	+	0.931359i	$0.381376\pi$
$192$	−13.2305	+	4.11754i	−0.954828	+	0.297158i
$193$	−3.26855	+	5.66129i	−0.235275	+	0.407509i	−0.959353	−	0.282210i	$-0.908932\pi$
$193$	−3.26855	+	5.66129i	−0.235275	+	0.407509i	0.724077	+	0.689719i	$0.242266\pi$
$194$	−10.1136	+	5.46905i	−0.726116	+	0.392655i
$195$	−13.4313	−	8.76566i	−0.961833	−	0.627722i
$196$	4.20622	−	13.3532i	0.300444	−	0.953799i
$197$		−	9.67868i		−	0.689577i	−0.938680	−	0.344789i	$-0.887951\pi$
$197$		−	9.67868i		−	0.689577i	0.938680	−	0.344789i	$-0.112049\pi$
$198$	−12.2292	−	1.68751i	−0.869091	−	0.119926i
$199$	−12.4723			−0.884141			−0.442071	−	0.896980i	$-0.645756\pi$
$199$	−12.4723			−0.884141			−0.442071	+	0.896980i	$0.645756\pi$
$200$	−0.0795719	−	0.169035i	−0.00562658	−	0.0119526i
$201$	0.634364	−	11.6018i	0.0447446	−	0.818328i
$202$	4.99708	+	9.24083i	0.351593	+	0.650182i
$203$	3.22415	−	7.92230i	0.226291	−	0.556036i
$204$	9.40689	+	21.4541i	0.658614	+	1.50208i
$205$	22.9862	−	13.2711i	1.60542	−	0.926892i
$206$	1.35413	−	2.20135i	0.0943470	−	0.153376i
$207$	22.8438	−	10.0471i	1.58776	−	0.698319i
$208$	−9.89270	+	13.4236i	−0.685935	+	0.930758i
$209$	8.15155	−	4.70630i	0.563854	−	0.325541i
$210$	7.86725	+	12.0554i	0.542891	+	0.831900i
$211$	−2.99518	+	5.18780i	−0.206196	+	0.357143i	−0.950513	−	0.310684i	$-0.899442\pi$
$211$	−2.99518	+	5.18780i	−0.206196	+	0.357143i	0.744317	+	0.667827i	$0.232775\pi$
$212$	−0.271122	+	4.85784i	−0.0186208	+	0.333638i
$213$	2.33458	+	4.60763i	0.159963	+	0.315709i
$214$	10.0320	+	0.279731i	0.685771	+	0.0191220i
$215$	15.2479			1.03990
$216$	3.60049	−	14.2491i	0.244982	−	0.969528i
$217$	−1.91836	−	13.9049i	−0.130227	−	0.943929i
$218$	−0.0576356	+	2.06698i	−0.00390357	+	0.139993i
$219$	−3.00330	−	5.92744i	−0.202944	−	0.400539i
$220$	12.9065	+	0.720330i	0.870157	+	0.0485646i
$221$	24.4141	+	14.0955i	1.64227	+	0.948167i
$222$	9.72274	+	20.5937i	0.652548	+	1.38216i
$223$	−10.2848	−	17.8138i	−0.688723	−	1.19290i	−0.972251	−	0.233939i	$-0.924838\pi$
$223$	−10.2848	−	17.8138i	−0.688723	−	1.19290i	0.283528	−	0.958964i	$-0.408495\pi$
$224$	12.9786	−	7.45365i	0.867167	−	0.498018i
$225$	0.196979	+	0.0216055i	0.0131319	+	0.00144037i
$226$	−12.3631	+	20.0981i	−0.822379	+	1.33690i
$227$	6.62731	−	3.82628i	0.439870	−	0.253959i	−0.263673	−	0.964612i	$-0.584934\pi$
$227$	6.62731	−	3.82628i	0.439870	−	0.253959i	0.703542	+	0.710653i	$0.251601\pi$
$228$	4.49982	+	10.2626i	0.298008	+	0.679659i
$229$	2.80807	−	4.86372i	0.185563	−	0.321404i	−0.758203	−	0.652018i	$-0.773923\pi$
$229$	2.80807	−	4.86372i	0.185563	−	0.321404i	0.943766	+	0.330614i	$0.107256\pi$
$230$	−22.9857	+	12.4298i	−1.51563	+	0.819594i
$231$	13.2889	−	1.09847i	0.874344	−	0.0722739i
$232$	8.27299	−	3.89445i	0.543148	−	0.255683i
$233$	−11.1326			−0.729322			−0.364661	−	0.931140i	$-0.618815\pi$
$233$	−11.1326			−0.729322			−0.364661	+	0.931140i	$0.618815\pi$
$234$	−6.66653	−	16.3821i	−0.435804	−	1.07093i
$235$	−4.81784			−0.314281
$236$	−2.27849	−	1.49069i	−0.148317	−	0.0970354i
$237$	−9.46512	+	14.5030i	−0.614826	+	0.942073i
$238$	−14.9645	−	20.4032i	−0.970007	−	1.32254i
$239$	0.0961982	+	0.0555401i	0.00622255	+	0.00359259i	0.503108	−	0.864224i	$-0.332190\pi$
$239$	0.0961982	+	0.0555401i	0.00622255	+	0.00359259i	−0.496885	+	0.867816i	$0.665523\pi$
$240$	−2.54488	+	15.1774i	−0.164272	+	0.979696i
$241$	−21.0510	+	12.1538i	−1.35601	+	0.782893i	−0.989083	−	0.147356i	$-0.952924\pi$
$241$	−21.0510	+	12.1538i	−1.35601	+	0.782893i	−0.366927	+	0.930250i	$0.619590\pi$
$242$	−1.87709	+	3.05150i	−0.120664	+	0.196158i
$243$	10.8972	+	11.1468i	0.699058	+	0.715065i
$244$	7.85122	+	15.5390i	0.502623	+	0.994785i
$245$	−11.1300	−	10.8575i	−0.711072	−	0.693661i
$246$	29.1699	+	2.41200i	1.85980	+	0.153784i
$247$	11.6786	+	6.74264i	0.743091	+	0.429024i
$248$	8.56222	−	12.3233i	0.543702	−	0.782527i
$249$	6.74405	−	10.3336i	0.427387	−	0.654868i
$250$	−15.9079	−	0.443576i	−1.00610	−	0.0280542i
$251$			12.5116i			0.789728i	0.918740	+	0.394864i	$0.129208\pi$
$251$			12.5116i			0.789728i	−0.918740	+	0.394864i	$0.870792\pi$
$252$	−0.442904	+	15.8683i	−0.0279003	+	0.999611i
$253$			24.2050i			1.52176i
$254$	−0.153700	+	5.51212i	−0.00964397	+	0.345861i
$255$	25.9784	+	1.42045i	1.62683	+	0.0889520i
$256$	15.6038	+	3.53872i	0.975235	+	0.221170i
$257$	0.869846	+	0.502206i	0.0542595	+	0.0313268i	0.526884	−	0.849937i	$-0.323360\pi$
$257$	0.869846	+	0.502206i	0.0542595	+	0.0313268i	−0.472625	+	0.881264i	$0.656693\pi$
$258$	13.8196	+	9.57873i	0.860369	+	0.596346i
$259$	−15.0951	−	19.4219i	−0.937961	−	1.20682i
$260$	8.35174	+	16.5297i	0.517953	+	1.02513i
$261$	−1.05743	+	9.64065i	−0.0654530	+	0.596741i
$262$	9.42313	+	5.79652i	0.582163	+	0.358110i
$263$	−0.561785	+	0.324347i	−0.0346412	+	0.0200001i	−0.517221	−	0.855852i	$-0.673033\pi$
$263$	−0.561785	+	0.324347i	−0.0346412	+	0.0200001i	0.482579	+	0.875852i	$0.339700\pi$
$264$	11.2450	+	8.76074i	0.692083	+	0.539186i
$265$	4.67968	+	2.70182i	0.287471	+	0.165971i
$266$	−7.15834	−	9.75994i	−0.438906	−	0.598420i
$267$	−13.1425	−	25.9386i	−0.804309	−	1.58742i
$268$	−7.34536	+	11.2273i	−0.448689	+	0.685814i
$269$	−9.94095			−0.606111			−0.303055	−	0.952973i	$-0.598007\pi$
$269$	−9.94095			−0.606111			−0.303055	+	0.952973i	$0.598007\pi$
$270$	−12.3215	−	10.7058i	−0.749863	−	0.651532i
$271$	−14.6487			−0.889844			−0.444922	−	0.895569i	$-0.646769\pi$
$271$	−14.6487			−0.889844			−0.444922	+	0.895569i	$0.646769\pi$
$272$	3.00999	−	26.8817i	0.182507	−	1.62995i
$273$	10.8823	+	15.7012i	0.658626	+	0.950278i
$274$	6.02212	+	11.1364i	0.363810	+	0.672774i
$275$	−0.0961000	+	0.166450i	−0.00579505	+	0.0100373i
$276$	−28.6410	−	3.17421i	−1.72398	−	0.191065i
$277$	−2.29551	+	1.32531i	−0.137924	+	0.0796302i	−0.567374	−	0.823460i	$-0.692041\pi$
$277$	−2.29551	+	1.32531i	−0.137924	+	0.0796302i	0.429450	+	0.903090i	$0.358707\pi$
$278$	−2.53608	−	1.56004i	−0.152104	−	0.0935649i
$279$	6.40775	+	14.5692i	0.383622	+	0.872235i
$280$	−0.888316	−	16.5986i	−0.0530870	−	0.991953i
$281$	10.4403	+	18.0831i	0.622815	+	1.07875i	0.988959	+	0.148189i	$0.0473442\pi$
$281$	10.4403	+	18.0831i	0.622815	+	1.07875i	−0.366145	+	0.930558i	$0.619322\pi$
$282$	−4.36654	−	3.02657i	−0.260024	−	0.180230i
$283$	8.81643	+	5.09017i	0.524082	+	0.302579i	0.738603	−	0.674140i	$-0.235486\pi$
$283$	8.81643	+	5.09017i	0.524082	+	0.302579i	−0.214521	+	0.976719i	$0.568819\pi$
$284$	0.332363	−	5.95513i	0.0197221	−	0.353372i
$285$	12.4269	+	0.679477i	0.736104	+	0.0402488i
$286$	17.1479	+	0.478152i	1.01398	+	0.0282737i
$287$	−31.3180	+	4.32070i	−1.84864	+	0.255043i
$288$	−11.8409	+	12.1570i	−0.697734	+	0.716357i
$289$	−28.7305			−1.69003
$290$	0.283061	−	10.1514i	0.0166219	−	0.596110i
$291$	−7.69615	+	11.7925i	−0.451156	+	0.691289i
$292$	−0.427566	+	7.66092i	−0.0250214	+	0.448321i
$293$	−8.34533	+	14.4545i	−0.487539	+	0.844443i	−0.999897	−	0.0143292i	$-0.995439\pi$
$293$	−8.34533	+	14.4545i	−0.487539	+	0.844443i	0.512358	+	0.858772i	$0.328772\pi$
$294$	−3.26676	−	16.8324i	−0.190521	−	0.981683i
$295$	−2.61887	+	1.51201i	−0.152477	+	0.0880324i
$296$	2.19662	−	26.2046i	0.127676	−	1.52311i
$297$	−14.1518	+	5.32238i	−0.821171	+	0.308836i
$298$	8.18917	+	5.03747i	0.474386	+	0.291813i
$299$	−30.0321	+	17.3391i	−1.73680	+	1.00274i
$300$	−0.184352	−	0.135540i	−0.0106436	−	0.00782540i
$301$	−16.8222	−	6.84614i	−0.969613	−	0.394605i
$302$	5.15983	−	2.79023i	0.296915	−	0.160560i
$303$	10.7748	+	7.03198i	0.618997	+	0.403977i
$304$	1.43984	−	12.8590i	0.0825804	−	0.737513i
$305$	19.3358			1.10717
$306$	22.6526	+	17.6071i	1.29496	+	1.00653i
$307$		−	27.1942i		−	1.55205i	−0.630700	−	0.776027i	$-0.717232\pi$
$307$		−	27.1942i		−	1.55205i	0.630700	−	0.776027i	$-0.282768\pi$
$308$	−13.9156	−	6.58959i	−0.792917	−	0.375477i
$309$	0.172817	−	3.16063i	0.00983123	−	0.179802i
$310$	−7.92738	−	14.6597i	−0.450245	−	0.832614i
$311$	−6.34694	+	10.9932i	−0.359902	+	0.623369i	−0.987944	−	0.154811i	$-0.950523\pi$
$311$	−6.34694	+	10.9932i	−0.359902	+	0.623369i	0.628042	+	0.778179i	$0.283857\pi$
$312$	−2.81453	+	20.2278i	−0.159342	+	1.14518i
$313$	−5.78126	+	3.33781i	−0.326776	+	0.188664i	−0.654409	−	0.756141i	$-0.727083\pi$
$313$	−5.78126	+	3.33781i	−0.326776	+	0.188664i	0.327633	+	0.944805i	$0.393749\pi$
$314$	−4.26227	+	6.92897i	−0.240534	+	0.391024i
$315$	15.5081	+	8.38672i	0.873783	+	0.472538i
$316$	17.8486	−	9.01818i	1.00406	−	0.507312i
$317$	24.7738	−	14.3031i	1.39143	−	0.803345i	0.397960	−	0.917403i	$-0.369718\pi$
$317$	24.7738	−	14.3031i	1.39143	−	0.803345i	0.993474	+	0.114058i	$0.0363850\pi$
$318$	2.54404	+	5.38851i	0.142663	+	0.302173i
$319$	−8.14647	−	4.70337i	−0.456115	−	0.263338i
$320$	11.3230	−	13.6953i	0.632977	−	0.765591i
$321$	10.9643	−	5.55536i	0.611968	−	0.310070i
$322$	30.9397	−	3.39274i	1.72420	−	0.189070i
$323$	−21.8754			−1.21718
$324$	−4.44194	−	17.4433i	−0.246775	−	0.969073i
$325$	−0.275362			−0.0152743
$326$	−17.8513	−	0.497765i	−0.988693	−	0.0275687i
$327$	1.14462	+	2.25908i	0.0632978	+	0.124927i
$328$	−27.7555	−	19.2846i	−1.53254	−	1.06481i
$329$	5.31526	+	2.16316i	0.293040	+	0.119259i
$330$	14.3164	−	6.75911i	0.788093	−	0.372077i
$331$	4.52326	+	7.83452i	0.248621	+	0.430624i	0.963143	−	0.268988i	$-0.0866893\pi$
$331$	4.52326	+	7.83452i	0.248621	+	0.430624i	−0.714522	+	0.699613i	$0.753356\pi$
$332$	−12.7174	+	6.42559i	−0.697960	+	0.352650i
$333$	22.4904	+	16.4963i	1.23247	+	0.903993i
$334$	5.47023	−	8.89270i	0.299318	−	0.486587i
$335$	7.45041	+	12.9045i	0.407060	+	0.705048i
$336$	9.62212	−	15.6018i	0.524930	−	0.851146i
$337$	6.14587	−	10.6450i	0.334787	−	0.579868i	−0.648657	−	0.761081i	$-0.724669\pi$
$337$	6.14587	−	10.6450i	0.334787	−	0.579868i	0.983444	+	0.181213i	$0.0580023\pi$
$338$	2.94548	+	5.44692i	0.160213	+	0.296274i
$339$	−1.57780	+	28.8561i	−0.0856942	+	1.56725i
$340$	−25.1398	−	16.4475i	−1.36339	−	0.891991i
$341$	−15.4373			−0.835977
$342$	10.8360	+	8.42240i	0.585942	+	0.455431i
$343$	7.40426	+	16.9758i	0.399793	+	0.916606i
$344$	−8.26944	−	17.5668i	−0.445858	−	0.947139i
$345$	−17.4914	+	26.8014i	−0.941705	+	1.44294i
$346$	4.35447	+	8.05249i	0.234098	+	0.432905i
$347$	12.6774	−	21.9579i	0.680557	−	1.17876i	−0.294254	−	0.955727i	$-0.595071\pi$
$347$	12.6774	−	21.9579i	0.680557	−	1.17876i	0.974811	−	0.223032i	$-0.0715955\pi$
$348$	6.63365	−	9.02265i	0.355601	−	0.483665i
$349$	−2.10659	−	3.64873i	−0.112763	−	0.195312i	0.804120	−	0.594467i	$-0.202637\pi$
$349$	−2.10659	−	3.64873i	−0.112763	−	0.195312i	−0.916883	+	0.399155i	$0.869304\pi$
$350$	0.226233	+	0.0995077i	0.0120926	+	0.00531891i
$351$	−16.7412	−	13.7461i	−0.893580	−	0.733711i
$352$	−6.16976	−	15.2600i	−0.328849	−	0.813363i
$353$	15.5589	−	8.98292i	0.828116	−	0.478113i	−0.0250915	−	0.999685i	$-0.507988\pi$
$353$	15.5589	−	8.98292i	0.828116	−	0.478113i	0.853207	+	0.521572i	$0.174654\pi$
$354$	−3.32340	−	0.274805i	−0.176637	−	0.0146057i
$355$	−5.73673	−	3.31210i	−0.304474	−	0.175788i
$356$	−1.87104	+	33.5244i	−0.0991649	+	1.77679i
$357$	−28.0228	−	13.2311i	−1.48312	−	0.700266i
$358$	9.30826	+	0.259551i	0.491957	+	0.0137177i
$359$		−	1.27422i		−	0.0672506i	−0.999435	−	0.0336253i	$-0.989295\pi$
$359$		−	1.27422i		−	0.0672506i	0.999435	−	0.0336253i	$-0.0107053\pi$
$360$	6.12040	+	17.8265i	0.322573	+	0.939540i
$361$	8.53584			0.449255
$362$	−30.2746	−	0.844175i	−1.59120	−	0.0443688i
$363$	−0.239558	+	4.38125i	−0.0125735	+	0.229956i
$364$	−1.79238	−	21.9861i	−0.0939462	−	1.15239i
$365$	7.37996	+	4.26082i	0.386285	+	0.223022i
$366$	17.5246	+	12.1468i	0.916024	+	0.634922i
$367$	12.5985	+	21.8212i	0.657636	+	1.13906i	0.981226	+	0.192862i	$0.0617768\pi$
$367$	12.5985	+	21.8212i	0.657636	+	1.13906i	−0.323590	+	0.946197i	$0.604890\pi$
$368$	26.7860	+	19.7403i	1.39632	+	1.02904i
$369$	32.8141	−	14.4321i	1.70823	−	0.751306i
$370$	−24.8759	−	15.3021i	−1.29324	−	0.795518i
$371$	−3.94975	−	5.08190i	−0.205061	−	0.263839i
$372$	2.02443	−	18.2664i	0.104962	−	0.947071i
$373$	−17.5507	−	10.1329i	−0.908741	−	0.524662i	−0.0287154	−	0.999588i	$-0.509142\pi$
$373$	−17.5507	−	10.1329i	−0.908741	−	0.524662i	−0.880026	+	0.474926i	$0.842475\pi$
$374$	−24.4778	+	13.2367i	−1.26572	+	0.684451i
$375$	−17.3863	+	8.80926i	−0.897826	+	0.454908i
$376$	2.61288	+	5.55055i	0.134749	+	0.286248i
$377$		−	13.4769i		−	0.694095i
$378$	8.78687	+	17.3433i	0.451948	+	0.892044i
$379$	31.4979			1.61794			0.808968	−	0.587852i	$-0.200026\pi$
$379$	31.4979			1.61794			0.808968	+	0.587852i	$0.200026\pi$
$380$	−12.0257	−	7.86773i	−0.616905	−	0.403606i
$381$	3.05242	+	6.02439i	0.156380	+	0.308639i
$382$	5.16997	−	2.79571i	0.264518	−	0.143041i
$383$	2.45844	−	4.25815i	0.125621	−	0.217581i	−0.796355	−	0.604830i	$-0.793241\pi$
$383$	2.45844	−	4.25815i	0.125621	−	0.217581i	0.921975	+	0.387249i	$0.126574\pi$
$384$	18.8658	−	5.29929i	0.962740	−	0.270428i
$385$	−13.5018	+	10.4939i	−0.688116	+	0.534817i
$386$	4.84379	−	7.87432i	0.246542	−	0.400792i
$387$	20.4709	+	2.24533i	1.04059	+	0.114137i
$388$	14.5128	−	7.33273i	0.736778	−	0.372263i
$389$	−8.15128	+	4.70615i	−0.413286	+	0.238611i	−0.692201	−	0.721705i	$-0.743359\pi$
$389$	−8.15128	+	4.70615i	−0.413286	+	0.238611i	0.278914	+	0.960316i	$0.410025\pi$
$390$	18.6418	+	12.9211i	0.943963	+	0.654287i
$391$	28.1268	−	48.7171i	1.42243	−	2.46373i
$392$	−6.47255	+	18.7111i	−0.326913	+	0.945054i
$393$	13.5294	+	0.739762i	0.682469	+	0.0373161i
$394$	−0.381519	+	13.6824i	−0.0192207	+	0.689309i
$395$		−	22.2098i		−	1.11749i
$396$	17.2214	+	2.86762i	0.865410	+	0.144104i
$397$	−13.7201			−0.688590			−0.344295	−	0.938862i	$-0.611882\pi$
$397$	−13.7201			−0.688590			−0.344295	+	0.938862i	$0.611882\pi$
$398$	17.6317	+	0.491642i	0.883798	+	0.0246438i
$399$	−13.4048	−	6.32917i	−0.671080	−	0.316855i
$400$	0.105825	+	0.242095i	0.00529124	+	0.0121048i
$401$	−5.11798	+	8.86460i	−0.255580	+	0.442677i	−0.965053	−	0.262056i	$-0.915600\pi$
$401$	−5.11798	+	8.86460i	−0.255580	+	0.442677i	0.709473	+	0.704732i	$0.248933\pi$
$402$	−1.35410	+	16.3760i	−0.0675366	+	0.816763i
$403$	−11.0584	−	19.1537i	−0.550858	−	0.954114i
$404$	−6.69993	−	13.2604i	−0.333334	−	0.659730i
$405$	−19.5159	−	4.33331i	−0.969755	−	0.215324i
$406$	−4.87015	+	11.0724i	−0.241702	+	0.549513i
$407$	−23.4283	+	13.5264i	−1.16130	+	0.670477i
$408$	−12.4525	−	30.6996i	−0.616491	−	1.51986i
$409$	16.4287	+	9.48511i	0.812347	+	0.469009i	0.847770	−	0.530364i	$-0.177945\pi$
$409$	16.4287	+	9.48511i	0.812347	+	0.469009i	−0.0354235	+	0.999372i	$0.511278\pi$
$410$	−33.0178	+	17.8548i	−1.63064	+	0.881783i
$411$	12.9850	+	8.47444i	0.640505	+	0.418013i
$412$	−2.00107	+	3.05860i	−0.0985854	+	0.150686i
$413$	3.56813	−	0.492268i	0.175576	−	0.0242229i
$414$	−32.6896	+	13.3027i	−1.60660	+	0.653792i
$415$			15.8248i			0.776809i
$416$	14.5141	−	18.5865i	0.711612	−	0.911277i
$417$	−3.64123	−	0.199095i	−0.178312	−	0.00974973i
$418$	−11.7091	+	6.33180i	−0.572709	+	0.309699i
$419$	−11.0262	−	6.36600i	−0.538667	−	0.311000i	0.205872	−	0.978579i	$-0.433997\pi$
$419$	−11.0262	−	6.36600i	−0.538667	−	0.311000i	−0.744539	+	0.667579i	$0.767330\pi$
$420$	−10.6464	−	17.3524i	−0.519493	−	0.846709i
$421$	1.49213	−	0.861482i	0.0727220	−	0.0419861i	−0.463198	−	0.886255i	$-0.653298\pi$
$421$	1.49213	−	0.861482i	0.0727220	−	0.0419861i	0.535920	+	0.844269i	$0.319965\pi$
$422$	4.43867	−	7.21574i	0.216071	−	0.351257i
$423$	−6.46815	−	0.709452i	−0.314492	−	0.0344948i
$424$	0.574765	−	6.85667i	0.0279131	−	0.332989i
$425$	0.386838	−	0.223341i	0.0187644	−	0.0108336i
$426$	−3.11869	−	6.60566i	−0.151101	−	0.320045i
$427$	−21.3322	−	8.68158i	−1.03234	−	0.420131i
$428$	−14.1708	−	0.790891i	−0.684972	−	0.0382292i
$429$	18.7416	−	9.49593i	0.904852	−	0.458468i
$430$	−21.5554	−	0.601049i	−1.03949	−	0.0289852i
$431$		−	29.1042i		−	1.40190i	−0.713210	−	0.700951i	$-0.752759\pi$
$431$		−	29.1042i		−	1.40190i	0.713210	−	0.700951i	$-0.247241\pi$
$432$	−5.65156	+	20.0015i	−0.271911	+	0.962323i
$433$			27.2599i			1.31003i	0.755618	+	0.655013i	$0.227337\pi$
$433$			27.2599i			1.31003i	−0.755618	+	0.655013i	$0.772663\pi$
$434$	2.16380	+	19.7325i	0.103866	+	0.947192i
$435$	−5.62149	−	11.0948i	−0.269530	−	0.531956i
$436$	0.162955	−	2.91974i	0.00780411	−	0.139830i
$437$	13.4546	−	23.3040i	0.643619	−	1.11478i
$438$	4.01201	+	8.49780i	0.191701	+	0.406041i
$439$	−5.76611	−	9.98719i	−0.275201	−	0.476663i	0.694985	−	0.719025i	$-0.255411\pi$
$439$	−5.76611	−	9.98719i	−0.275201	−	0.476663i	−0.970186	+	0.242362i	$0.922078\pi$
$440$	−18.2171	−	1.52706i	−0.868466	−	0.0727997i
$441$	−13.3437	−	16.2156i	−0.635414	−	0.772171i
$442$	−33.9578	−	20.8887i	−1.61521	−	0.993574i
$443$	7.52816	+	13.0391i	0.357674	+	0.619509i	0.987572	−	0.157169i	$-0.0502367\pi$
$443$	7.52816	+	13.0391i	0.357674	+	0.619509i	−0.629898	+	0.776678i	$0.716903\pi$
$444$	−12.9329	−	29.4958i	−0.613769	−	1.39981i
$445$	32.2949	+	18.6455i	1.53093	+	0.883880i
$446$	13.8371	+	25.5882i	0.655205	+	1.21164i
$447$	11.7577	+	0.642891i	0.556122	+	0.0304077i
$448$	−18.6411	+	10.0254i	−0.880711	+	0.473654i
$449$	1.46659			0.0692128			0.0346064	−	0.999401i	$-0.488982\pi$
$449$	1.46659			0.0692128			0.0346064	+	0.999401i	$0.488982\pi$
$450$	−0.277611	−	0.0383075i	−0.0130867	−	0.00180583i
$451$			34.7693i			1.63722i
$452$	18.2695	−	27.9246i	0.859323	−	1.31346i
$453$	3.92647	−	6.01637i	0.184482	−	0.282674i
$454$	−9.51961	+	5.14783i	−0.446778	+	0.241600i
$455$	−22.6921	−	9.23504i	−1.06382	−	0.432945i
$456$	−5.95670	−	14.6853i	−0.278948	−	0.687701i
$457$	17.6400	+	30.5535i	0.825167	+	1.42923i	0.901792	+	0.432171i	$0.142252\pi$
$457$	17.6400	+	30.5535i	0.825167	+	1.42923i	−0.0766253	+	0.997060i	$0.524415\pi$
$458$	−4.16139	+	6.76498i	−0.194449	+	0.316107i
$459$	34.6679	+	5.73247i	1.61816	+	0.267569i
$460$	32.9840	−	16.6654i	1.53789	−	0.777031i
$461$	8.11884	+	14.0622i	0.378132	+	0.654944i	0.990790	−	0.135404i	$-0.0432332\pi$
$461$	8.11884	+	14.0622i	0.378132	+	0.654944i	−0.612658	+	0.790348i	$0.709900\pi$
$462$	−18.8293	+	1.02904i	−0.876019	+	0.0478751i
$463$	−10.1405	−	5.85463i	−0.471270	−	0.272088i	0.245501	−	0.969396i	$-0.421047\pi$
$463$	−10.1405	−	5.85463i	−0.471270	−	0.272088i	−0.716771	+	0.697308i	$0.754381\pi$
$464$	−11.8487	+	5.17933i	−0.550064	+	0.240444i
$465$	−17.0932	−	11.1556i	−0.792678	−	0.517326i
$466$	15.7378	+	0.438831i	0.729038	+	0.0203285i
$467$		−	13.0202i		−	0.602504i	−0.953545	−	0.301252i	$-0.902595\pi$
$467$		−	13.0202i		−	0.602504i	0.953545	−	0.301252i	$-0.0974046\pi$
$468$	8.77847	+	23.4216i	0.405785	+	1.08266i
$469$	−2.42565	−	17.5820i	−0.112006	−	0.811861i
$470$	6.81081	+	0.189912i	0.314159	+	0.00876000i
$471$	−0.543959	+	9.94839i	−0.0250643	+	0.458398i
$472$	3.16226	+	2.19714i	0.145555	+	0.101132i
$473$	−9.98710	+	17.2982i	−0.459208	+	0.795371i
$474$	13.9522	−	20.1293i	0.640845	−	0.924570i
$475$	0.185046	−	0.106836i	0.00849047	−	0.00490198i
$476$	20.3506	+	29.4331i	0.932766	+	1.34907i
$477$	5.88480	+	4.31640i	0.269447	+	0.197635i
$478$	−0.133803	−	0.0823070i	−0.00611999	−	0.00376464i
$479$	−10.2441	−	17.7433i	−0.468065	−	0.810713i	0.531269	−	0.847203i	$-0.321716\pi$
$479$	−10.2441	−	17.7433i	−0.468065	−	0.810713i	−0.999334	+	0.0364903i	$0.988382\pi$
$480$	4.19588	−	21.3554i	0.191515	−	0.974737i
$481$	−33.5654	−	19.3790i	−1.53045	−	0.883606i
$482$	30.2381	−	16.3516i	1.37731	−	0.744793i
$483$	31.3308	−	21.7150i	1.42560	−	0.988068i
$484$	2.77386	−	4.23981i	0.126085	−	0.192718i
$485$		−	18.0589i		−	0.820012i
$486$	−14.9656	−	16.1873i	−0.678855	−	0.734272i
$487$		−	35.1878i		−	1.59451i	−0.603642	−	0.797255i	$-0.706285\pi$
$487$		−	35.1878i		−	1.59451i	0.603642	−	0.797255i	$-0.293715\pi$
$488$	−10.4865	−	22.2765i	−0.474700	−	1.00841i
$489$	−19.5104	+	9.88545i	−0.882289	+	0.447036i
$490$	15.3062	+	15.7876i	0.691462	+	0.713211i
$491$	6.58117	−	11.3989i	0.297004	−	0.514426i	−0.678445	−	0.734651i	$-0.737346\pi$
$491$	6.58117	−	11.3989i	0.297004	−	0.514426i	0.975449	+	0.220225i	$0.0706791\pi$
$492$	−41.1413	−	4.55959i	−1.85479	−	0.205562i
$493$	10.9309	+	18.9328i	0.492302	+	0.852692i
$494$	−16.2438	−	9.99218i	−0.730844	−	0.449569i
$495$	11.4680	−	15.6350i	0.515449	−	0.702741i
$496$	−12.5899	+	17.0834i	−0.565302	+	0.767069i
$497$	4.84192	+	6.22979i	0.217190	+	0.279444i
$498$	−9.94116	+	14.3424i	−0.445474	+	0.642701i
$499$	7.07527	−	12.2547i	0.316733	−	0.548597i	−0.663072	−	0.748556i	$-0.730747\pi$
$499$	7.07527	−	12.2547i	0.316733	−	0.548597i	0.979804	+	0.199959i	$0.0640808\pi$
$500$	22.4710	+	1.25413i	1.00493	+	0.0560866i
$501$	0.698121	−	12.7678i	0.0311898	−	0.570425i
$502$	0.493191	−	17.6873i	0.0220122	−	0.789421i
$503$	5.20784			0.232206			0.116103	−	0.993237i	$-0.462960\pi$
$503$	5.20784			0.232206			0.116103	+	0.993237i	$0.462960\pi$
$504$	1.25162	−	22.4150i	0.0557518	−	0.998445i
$505$	−16.5004			−0.734260
$506$	0.954126	−	34.2177i	0.0424161	−	1.52116i
$507$	6.35112	+	4.14494i	0.282063	+	0.184083i
$508$	0.434559	−	7.78622i	0.0192804	−	0.345458i
$509$	−1.19121	+	2.06323i	−0.0527994	+	0.0914513i	−0.891217	−	0.453577i	$-0.850148\pi$
$509$	−1.19121	+	2.06323i	−0.0527994	+	0.0914513i	0.838418	+	0.545028i	$0.183481\pi$
$510$	−36.6688	−	3.03207i	−1.62372	−	0.134262i
$511$	−6.22885	−	8.01426i	−0.275548	−	0.354530i
$512$	−21.9190	−	5.61764i	−0.968692	−	0.248267i
$513$	16.5835	+	2.74215i	0.732180	+	0.121069i
$514$	−1.20987	−	0.744239i	−0.0533653	−	0.0328270i
$515$	2.02968	+	3.51552i	0.0894386	+	0.154912i
$516$	−19.1586	−	14.0859i	−0.843412	−	0.620095i
$517$	3.15561	−	5.46567i	0.138783	−	0.240380i
$518$	20.5738	+	28.0510i	0.903959	+	1.23249i
$519$	9.38922	+	6.12769i	0.412141	+	0.268976i
$520$	−11.1550	−	23.6966i	−0.489178	−	1.03916i
$521$		−	34.3187i		−	1.50353i	−0.659432	−	0.751764i	$-0.729203\pi$
$521$		−	34.3187i		−	1.50353i	0.659432	−	0.751764i	$-0.270797\pi$
$522$	1.87486	−	13.5870i	0.0820606	−	0.594685i
$523$		−	5.75324i		−	0.251572i	−0.992057	−	0.125786i	$-0.959855\pi$
$523$		−	5.75324i		−	0.251572i	0.992057	−	0.125786i	$-0.0401452\pi$
$524$	−13.0926	−	8.56577i	−0.571955	−	0.374198i
$525$	0.301666	−	0.0249359i	0.0131658	−	0.00108829i
$526$	0.806961	−	0.436373i	0.0351852	−	0.0190268i
$527$	31.0705	+	17.9386i	1.35345	+	0.781416i
$528$	−15.5513	−	12.8280i	−0.676785	−	0.558267i
$529$	23.0992	+	40.0089i	1.00431	+	1.73952i
$530$	−6.50900	−	4.00393i	−0.282733	−	0.173919i
$531$	−3.73859	+	1.64429i	−0.162241	+	0.0713559i
$532$	9.73477	+	14.0794i	0.422056	+	0.610421i
$533$	−43.1397	+	24.9067i	−1.86859	+	1.07883i
$534$	17.5566	+	37.1866i	0.759750	+	1.60922i
$535$	−7.88147	+	13.6511i	−0.340746	+	0.590189i
$536$	10.8264	−	15.5820i	0.467631	−	0.673041i
$537$	10.1733	−	5.15460i	0.439012	−	0.222437i
$538$	14.0532	+	0.391858i	0.605875	+	0.0168942i
$539$	19.6074	−	5.51515i	0.844552	−	0.237554i
$540$	16.9965	+	15.6201i	0.731412	+	0.672180i
$541$		−	12.9750i		−	0.557839i	−0.960314	−	0.278919i	$-0.910024\pi$
$541$		−	12.9750i		−	0.557839i	0.960314	−	0.278919i	$-0.0899763\pi$
$542$	20.7083	+	0.577430i	0.889499	+	0.0248027i
$543$	−33.0882	+	16.7650i	−1.41995	+	0.719456i
$544$	−5.31475	+	37.8831i	−0.227868	+	1.62422i
$545$	−2.81266	−	1.62389i	−0.120481	−	0.0695599i
$546$	−14.7650	−	22.6252i	−0.631883	−	0.968267i
$547$	−12.2900	−	21.2870i	−0.525484	−	0.910165i	−0.999559	−	0.0296806i	$-0.990551\pi$
$547$	−12.2900	−	21.2870i	−0.525484	−	0.910165i	0.474076	−	0.880484i	$-0.342782\pi$
$548$	−8.07427	−	15.9805i	−0.344916	−	0.682653i
$549$	25.9591	+	2.84730i	1.10791	+	0.121520i
$550$	0.142414	−	0.231516i	0.00607257	−	0.00987189i
$551$	5.22882	+	9.05659i	0.222755	+	0.385824i
$552$	40.3636	+	5.61625i	1.71799	+	0.239043i
$553$	−9.97195	+	24.5028i	−0.424051	+	1.04197i
$554$	3.29732	−	1.78306i	0.140090	−	0.0757549i
$555$	−35.7160	−	1.95288i	−1.51606	−	0.0828953i
$556$	3.52368	+	2.30534i	0.149437	+	0.0977682i
$557$			28.0726i			1.18948i	0.803920	+	0.594738i	$0.202744\pi$
$557$			28.0726i			1.18948i	−0.803920	+	0.594738i	$0.797256\pi$
$558$	−8.48411	−	20.8485i	−0.359161	−	0.882589i
$559$	−28.6167			−1.21036
$560$	0.601489	+	23.4998i	0.0254176	+	0.993047i
$561$	−18.6269	+	28.5412i	−0.786427	+	1.20501i
$562$	−14.0462	−	25.9750i	−0.592505	−	1.09569i
$563$	−21.5471	−	12.4402i	−0.908104	−	0.524294i	−0.0282831	−	0.999600i	$-0.509004\pi$
$563$	−21.5471	−	12.4402i	−0.908104	−	0.524294i	−0.879821	+	0.475306i	$0.842337\pi$
$564$	6.05352	+	4.45068i	0.254899	+	0.187407i
$565$	−18.5308	−	32.0962i	−0.779595	−	1.35030i
$566$	−12.2628	−	7.54332i	−0.515445	−	0.317069i
$567$	19.5853	+	13.5432i	0.822504	+	0.568759i
$568$	−0.704593	+	8.40545i	−0.0295640	+	0.352685i
$569$	4.14553	+	7.18027i	0.173790	+	0.301013i	0.939742	−	0.341885i	$-0.111065\pi$
$569$	4.14553	+	7.18027i	0.173790	+	0.301013i	−0.765952	+	0.642898i	$0.777732\pi$
$570$	−17.5406	−	1.45040i	−0.734696	−	0.0607506i
$571$	−17.2447	+	29.8687i	−0.721668	+	1.24997i	0.238662	+	0.971103i	$0.423291\pi$
$571$	−17.2447	+	29.8687i	−0.721668	+	1.24997i	−0.960331	+	0.278864i	$0.910042\pi$
$572$	−24.2225	−	1.35189i	−1.01280	−	0.0565254i
$573$	3.93418	−	6.02819i	0.164353	−	0.251831i
$574$	44.4434	−	4.87351i	1.85503	−	0.203416i
$575$			0.549470i			0.0229145i
$576$	17.2183	−	16.7191i	0.717430	−	0.696630i
$577$			24.7248i			1.02931i	0.857398	+	0.514653i	$0.172079\pi$
$577$			24.7248i			1.02931i	−0.857398	+	0.514653i	$0.827921\pi$
$578$	40.6153	+	1.13252i	1.68937	+	0.0471064i
$579$	0.618173	−	11.3057i	0.0256904	−	0.469849i
$580$	−0.800305	+	14.3395i	−0.0332309	+	0.595415i
$581$	7.10517	−	17.4586i	0.294772	−	0.724307i
$582$	11.3446	−	16.3673i	0.470249	−	0.678445i
$583$	−6.13023	+	3.53929i	−0.253888	+	0.146582i
$584$	0.906417	−	10.8131i	0.0375078	−	0.447450i
$585$	27.6140	+	3.02882i	1.14170	+	0.125226i
$586$	12.3673	−	20.1049i	0.510887	−	0.830525i
$587$	5.15406	−	2.97570i	0.212731	−	0.122820i	−0.389849	−	0.920879i	$-0.627473\pi$
$587$	5.15406	−	2.97570i	0.212731	−	0.122820i	0.602580	+	0.798059i	$0.294140\pi$
$588$	3.95460	+	23.9241i	0.163085	+	0.986612i
$589$	14.8627	+	8.58097i	0.612406	+	0.353573i
$590$	3.76180	−	2.03424i	0.154871	−	0.0837482i
$591$	7.57685	+	14.9540i	0.311670	+	0.615125i
$592$	−4.13823	+	36.9580i	−0.170080	+	1.51896i
$593$			22.0022i			0.903521i	0.892139	+	0.451761i	$0.149204\pi$
$593$			22.0022i			0.903521i	−0.892139	+	0.451761i	$0.850796\pi$
$594$	20.2157	−	6.96621i	0.829460	−	0.285827i
$595$	39.3691	−	5.43145i	1.61397	−	0.222668i
$596$	−11.3782	−	7.44409i	−0.466068	−	0.304922i
$597$	19.2703	−	9.76384i	0.788682	−	0.399607i
$598$	43.1388	−	23.3278i	1.76408	−	0.953944i
$599$	2.08153	+	1.20177i	0.0850490	+	0.0491030i	0.541921	−	0.840429i	$-0.317697\pi$
$599$	2.08153	+	1.20177i	0.0850490	+	0.0491030i	−0.456872	+	0.889532i	$0.651030\pi$
$600$	0.255269	+	0.198875i	0.0104213	+	0.00811903i
$601$	−13.1755	+	7.60689i	−0.537441	+	0.310292i	−0.744041	−	0.668134i	$-0.767093\pi$
$601$	−13.1755	+	7.60689i	−0.537441	+	0.310292i	0.206600	+	0.978425i	$0.433760\pi$
$602$	23.5110	+	10.3412i	0.958237	+	0.421478i
$603$	8.10222	+	18.4219i	0.329948	+	0.750198i
$604$	−7.40425	+	3.74106i	−0.301275	+	0.152222i
$605$	−2.81354	−	4.87319i	−0.114387	−	0.198123i
$606$	−14.9548	−	10.3656i	−0.607497	−	0.421073i
$607$	−14.8303	+	25.6869i	−0.601945	+	1.04260i	0.390581	+	0.920569i	$0.372274\pi$
$607$	−14.8303	+	25.6869i	−0.601945	+	1.04260i	−0.992526	+	0.122031i	$0.961059\pi$
$608$	−2.54233	+	18.1215i	−0.103105	+	0.734925i
$609$	1.22043	+	14.7643i	0.0494542	+	0.598279i
$610$	−27.3344	−	0.762190i	−1.10674	−	0.0308602i
$611$	9.04197			0.365799
$612$	−31.3291	−	25.7834i	−1.26641	−	1.04223i
$613$			33.7214i			1.36199i	0.732287	+	0.680996i	$0.238453\pi$
$613$			33.7214i			1.36199i	−0.732287	+	0.680996i	$0.761547\pi$
$614$	−1.07195	+	38.4434i	−0.0432606	+	1.55145i
$615$	−25.1255	+	38.4989i	−1.01316	+	1.55242i
$616$	19.4123	+	9.86401i	0.782143	+	0.397432i
$617$	9.60104	−	16.6295i	0.386523	−	0.669478i	−0.605456	−	0.795879i	$-0.707009\pi$
$617$	9.60104	−	16.6295i	0.386523	−	0.669478i	0.991979	+	0.126401i	$0.0403426\pi$
$618$	−0.368893	+	4.46126i	−0.0148391	+	0.179458i
$619$	−28.9142	+	16.6936i	−1.16216	+	0.670974i	−0.951821	−	0.306654i	$-0.900791\pi$
$619$	−28.9142	+	16.6936i	−1.16216	+	0.670974i	−0.210340	+	0.977628i	$0.567457\pi$
$620$	10.6288	+	21.0363i	0.426862	+	0.844840i
$621$	−27.4295	+	33.4062i	−1.10071	+	1.34054i
$622$	9.40578	−	15.2905i	0.377137	−	0.613095i
$623$	−27.2576	−	35.0706i	−1.09205	−	1.40507i
$624$	4.77616	−	28.4844i	0.191199	−	1.14029i
$625$	12.3327	−	21.3608i	0.493307	−	0.854433i
$626$	8.30434	−	4.49066i	0.331908	−	0.179483i
$627$	−8.91023	+	13.6528i	−0.355840	+	0.545240i
$628$	6.29854	−	9.62722i	0.251339	−	0.384168i
$629$	62.8719			2.50687
$630$	−21.5927	−	12.4673i	−0.860272	−	0.496710i
$631$		−	38.4824i		−	1.53196i	−0.642865	−	0.765979i	$-0.722254\pi$
$631$		−	38.4824i		−	1.53196i	0.642865	−	0.765979i	$-0.277746\pi$
$632$	−25.5875	+	12.0451i	−1.01782	+	0.479128i
$633$	0.566471	−	10.3601i	0.0225152	−	0.411778i
$634$	−35.5856	+	19.2433i	−1.41328	+	0.764249i
$635$	−7.50067	−	4.33051i	−0.297655	−	0.171851i
$636$	−3.38401	−	7.71782i	−0.134185	−	0.306032i
$637$	20.8885	+	20.3770i	0.827633	+	0.807367i
$638$	11.3310	+	6.97011i	0.448598	+	0.275949i
$639$	−7.21406	−	5.29139i	−0.285384	−	0.209324i
$640$	−16.5468	+	18.9142i	−0.654070	+	0.747651i
$641$	8.65068	+	14.9834i	0.341681	+	0.591810i	0.984745	−	0.174003i	$-0.0556703\pi$
$641$	8.65068	+	14.9834i	0.341681	+	0.591810i	−0.643064	+	0.765813i	$0.722337\pi$
$642$	−15.7188	+	7.42122i	−0.620372	+	0.292892i
$643$	38.4329	+	22.1892i	1.51565	+	0.875058i	0.999831	+	0.0183580i	$0.00584386\pi$
$643$	38.4329	+	22.1892i	1.51565	+	0.875058i	0.515814	+	0.856700i	$0.327489\pi$
$644$	−43.8721	+	3.57660i	−1.72880	+	0.140938i
$645$	−23.5587	+	11.9366i	−0.927621	+	0.470005i
$646$	30.9244	+	0.862295i	1.21670	+	0.0339265i
$647$	42.9710			1.68937			0.844683	−	0.535267i	$-0.179789\pi$
$647$	42.9710			1.68937			0.844683	+	0.535267i	$0.179789\pi$
$648$	5.59183	+	24.8341i	0.219668	+	0.975575i
$649$		−	3.96135i		−	0.155497i
$650$	0.389269	+	0.0108544i	0.0152684	+	0.000425743i
$651$	13.8493	+	19.9820i	0.542796	+	0.783156i
$652$	25.2162	+	1.40735i	0.987541	+	0.0551159i
$653$	3.84289	+	2.21869i	0.150384	+	0.0868241i	0.573304	−	0.819343i	$-0.305662\pi$
$653$	3.84289	+	2.21869i	0.150384	+	0.0868241i	−0.422920	+	0.906167i	$0.638995\pi$
$654$	−1.52906	−	3.23869i	−0.0597911	−	0.126643i
$655$	−15.0485	+	8.68828i	−0.587995	+	0.339479i
$656$	38.4768	+	28.3560i	1.50227	+	1.10712i
$657$	9.28047	+	6.80706i	0.362065	+	0.265569i
$658$	−7.42873	−	3.26750i	−0.289602	−	0.127381i
$659$	−15.7290	−	27.2433i	−0.612713	−	1.06125i	−0.990781	−	0.135472i	$-0.956745\pi$
$659$	−15.7290	−	27.2433i	−0.612713	−	1.06125i	0.378068	−	0.925778i	$-0.376589\pi$
$660$	−20.5051	+	8.99079i	−0.798158	+	0.349966i
$661$	−12.9108	+	22.3622i	−0.502172	+	0.869788i	0.497825	+	0.867278i	$0.334132\pi$
$661$	−12.9108	+	22.3622i	−0.502172	+	0.869788i	−0.999997	+	0.00250996i	$0.999201\pi$
$662$	−6.08555	−	11.2537i	−0.236522	−	0.437387i
$663$	−48.7555	−	2.66585i	−1.89351	−	0.103533i
$664$	18.2315	−	8.58233i	0.707519	−	0.333059i
$665$	18.8323	−	2.59815i	0.730287	−	0.100752i
$666$	−31.1436	−	24.2068i	−1.20679	−	0.937994i
$667$	−26.8924			−1.04128
$668$	−8.08361	+	12.3557i	−0.312764	+	0.478055i
$669$	29.8359	+	19.4718i	1.15352	+	0.752824i
$670$	−10.0237	−	18.5363i	−0.387250	−	0.716120i
$671$	−12.6646	+	21.9358i	−0.488913	+	0.846822i
$672$	−14.2174	+	21.6764i	−0.548450	+	0.836183i
$673$	−11.9072	−	20.6238i	−0.458987	−	0.794989i	0.539920	−	0.841716i	$-0.318454\pi$
$673$	−11.9072	−	20.6238i	−0.458987	−	0.794989i	−0.998908	+	0.0467267i	$0.985121\pi$
$674$	−9.10780	+	14.8061i	−0.350820	+	0.570311i
$675$	−0.321255	+	0.120822i	−0.0123651	+	0.00465042i
$676$	−3.94921	−	7.81622i	−0.151893	−	0.300624i
$677$	9.66988	+	16.7487i	0.371644	+	0.643706i	0.989819	−	0.142335i	$-0.0454610\pi$
$677$	9.66988	+	16.7487i	0.371644	+	0.643706i	−0.618175	+	0.786041i	$0.712128\pi$
$678$	3.36794	−	40.7307i	0.129345	−	1.56425i
$679$	−8.10826	+	19.9234i	−0.311166	+	0.764590i
$680$	34.8908	+	24.2422i	1.33800	+	0.929647i
$681$	−7.24413	+	11.0999i	−0.277596	+	0.425349i
$682$	21.8232	+	0.608516i	0.835652	+	0.0233013i
$683$	7.10670			0.271930			0.135965	−	0.990714i	$-0.456586\pi$
$683$	7.10670			0.271930			0.135965	+	0.990714i	$0.456586\pi$
$684$	−14.9864	−	12.3336i	−0.573020	−	0.471586i
$685$	−19.8851			−0.759772
$686$	−9.79798	−	24.2899i	−0.374089	−	0.927393i
$687$	−0.531085	+	9.71294i	−0.0202621	+	0.370572i
$688$	10.9978	+	25.1595i	0.419285	+	0.959199i
$689$	−8.78268	−	5.07068i	−0.334593	−	0.193178i
$690$	25.7834	−	37.1986i	0.981558	−	1.41613i
$691$	8.65388	−	4.99632i	0.329209	−	0.190069i	−0.326281	−	0.945273i	$-0.605796\pi$
$691$	8.65388	−	4.99632i	0.329209	−	0.190069i	0.655490	+	0.755204i	$0.272462\pi$
$692$	−5.83834	−	11.5552i	−0.221940	−	0.439261i
$693$	−19.6720	+	12.1002i	−0.747277	+	0.459650i
$694$	−18.7871	+	30.5413i	−0.713148	+	1.15933i
$695$	4.05007	−	2.33831i	0.153628	−	0.0886972i
$696$	−9.73342	+	12.4935i	−0.368944	+	0.473565i
$697$	40.4028	−	69.9798i	1.53037	−	2.65067i
$698$	2.83419	+	5.24112i	0.107276	+	0.198379i
$699$	17.2004	−	8.71504i	0.650578	−	0.329633i
$700$	−0.315894	−	0.149588i	−0.0119397	−	0.00565390i
$701$		−	47.4191i		−	1.79099i	−0.445067	−	0.895497i	$-0.646820\pi$
$701$		−	47.4191i		−	1.79099i	0.445067	−	0.895497i	$-0.353180\pi$
$702$	23.1246	+	20.0922i	0.872782	+	0.758333i
$703$	30.0750			1.13430
$704$	8.12044	+	21.8158i	0.306051	+	0.822213i
$705$	7.44378	−	3.77159i	0.280349	−	0.142046i
$706$	−22.3491	+	12.0855i	−0.841120	+	0.454845i
$707$	18.2040	+	7.40852i	0.684633	+	0.278626i
$708$	4.68733	+	0.519486i	0.176161	+	0.0195235i
$709$	−24.0412	+	13.8802i	−0.902886	+	0.521281i	−0.878135	−	0.478412i	$-0.841212\pi$
$709$	−24.0412	+	13.8802i	−0.902886	+	0.521281i	−0.0247503	+	0.999694i	$0.507879\pi$
$710$	7.97925	+	4.90833i	0.299456	+	0.184206i
$711$	3.27050	−	29.8175i	0.122653	−	1.11824i
$712$	3.96650	−	47.3185i	0.148651	−	1.77333i
$713$	−38.2202	+	22.0664i	−1.43136	+	0.826394i
$714$	39.0933	+	19.8090i	1.46303	+	0.741334i
$715$	−13.4720	+	23.3342i	−0.503824	+	0.872650i
$716$	−13.1485	−	0.733836i	−0.491383	−	0.0274247i
$717$	−0.192110	−	0.0105042i	−0.00717446	−	0.000392286i
$718$	−0.0502277	+	1.80131i	−0.00187448	+	0.0672244i
$719$	39.0124			1.45492			0.727459	−	0.686151i	$-0.240701\pi$
$719$	39.0124			1.45492			0.727459	+	0.686151i	$0.240701\pi$
$720$	−7.94949	−	25.4420i	−0.296260	−	0.948166i
$721$	−0.660810	−	4.78979i	−0.0246098	−	0.178381i
$722$	−12.0668	−	0.336470i	−0.449080	−	0.0125221i
$723$	23.0102	−	35.2576i	0.855759	−	1.31125i
$724$	42.7648	+	2.38676i	1.58934	+	0.0887032i
$725$	−0.184930	−	0.106770i	−0.00686814	−	0.00396532i
$726$	0.511357	−	6.18417i	0.0189782	−	0.229516i
$727$	−17.5430	−	30.3853i	−0.650632	−	1.12693i	−0.982970	−	0.183767i	$-0.941171\pi$
$727$	−17.5430	−	30.3853i	−0.650632	−	1.12693i	0.332338	−	0.943160i	$-0.392163\pi$
$728$	1.66716	+	31.1516i	0.0617891	+	1.15456i
$729$	−25.5628	−	8.69146i	−0.946772	−	0.321906i
$730$	−10.2648	−	6.31428i	−0.379918	−	0.233702i
$731$	40.2018	−	23.2105i	1.48692	−	0.858473i
$732$	−24.2951	−	17.8623i	−0.897971	−	0.660208i
$733$	23.4014	−	40.5325i	0.864352	−	1.49710i	−0.00333678	−	0.999994i	$-0.501062\pi$
$733$	23.4014	−	40.5325i	0.864352	−	1.49710i	0.867689	−	0.497107i	$-0.165605\pi$
$734$	−16.9499	−	31.3445i	−0.625631	−	1.15695i
$735$	25.6961	+	8.06231i	0.947815	+	0.297383i
$736$	−37.0883	−	28.9621i	−1.36709	−	1.06756i
$737$	−19.5196			−0.719013
$738$	−46.9570	+	19.1087i	−1.72851	+	0.703400i
$739$	0.479066			0.0176227			0.00881137	−	0.999961i	$-0.497195\pi$
$739$	0.479066			0.0176227			0.00881137	+	0.999961i	$0.497195\pi$
$740$	34.5630	+	22.6126i	1.27056	+	0.831256i
$741$	−23.3224	−	1.27522i	−0.856768	−	0.0468464i
$742$	5.38330	+	7.33979i	0.197627	+	0.269452i
$743$	21.2339	+	12.2594i	0.778997	+	0.449754i	0.836075	−	0.548615i	$-0.184845\pi$
$743$	21.2339	+	12.2594i	0.778997	+	0.449754i	−0.0570775	+	0.998370i	$0.518178\pi$
$744$	−3.58189	+	25.7428i	−0.131319	+	0.943777i
$745$	−13.0779	+	7.55056i	−0.479139	+	0.276631i
$746$	24.4114	+	15.0164i	0.893764	+	0.549788i
$747$	−2.33029	+	21.2454i	−0.0852607	+	0.777330i
$748$	35.1252	−	17.7473i	1.28431	−	0.648906i
$749$	14.8244	−	11.5218i	0.541672	−	0.420998i
$750$	24.9257	−	11.7680i	0.910157	−	0.429706i
$751$	17.8407	+	10.3004i	0.651018	+	0.375865i	0.788846	−	0.614591i	$-0.210679\pi$
$751$	17.8407	+	10.3004i	0.651018	+	0.375865i	−0.137828	+	0.990456i	$0.544012\pi$
$752$	−3.47494	−	7.94961i	−0.126718	−	0.289893i
$753$	−9.79460	−	19.3310i	−0.356935	−	0.704463i
$754$	−0.531239	+	19.0518i	−0.0193466	+	0.693825i
$755$			9.21340i			0.335310i
$756$	−11.7380	−	24.8640i	−0.426908	−	0.904295i
$757$		−	1.42429i		−	0.0517668i	−0.999665	−	0.0258834i	$-0.991760\pi$
$757$		−	1.42429i		−	0.0517668i	0.999665	−	0.0258834i	$-0.00823986\pi$
$758$	−44.5274	−	1.24160i	−1.61731	−	0.0450969i
$759$	−18.9486	−	37.3978i	−0.687791	−	1.35745i
$760$	16.6902	+	11.5964i	0.605416	+	0.420644i
$761$	−12.8276	−	7.40604i	−0.465002	−	0.268469i	0.249143	−	0.968467i	$-0.419851\pi$
$761$	−12.8276	−	7.40604i	−0.465002	−	0.268469i	−0.714145	+	0.699998i	$0.753184\pi$
$762$	−4.07763	−	8.63679i	−0.147717	−	0.312878i
$763$	2.37395	+	3.05441i	0.0859427	+	0.110577i
$764$	−7.41880	+	3.74841i	−0.268403	+	0.135613i
$765$	−41.2498	+	18.1423i	−1.49139	+	0.655935i
$766$	−3.64326	+	5.92268i	−0.131636	+	0.213995i
$767$	4.91501	−	2.83768i	0.177471	−	0.102463i
$768$	−26.8788	+	6.74776i	−0.969904	+	0.243489i
$769$	40.5814	+	23.4297i	1.46340	+	0.844897i	0.999167	−	0.0408139i	$-0.0129951\pi$
$769$	40.5814	+	23.4297i	1.46340	+	0.844897i	0.464238	+	0.885711i	$0.346328\pi$
$770$	19.5007	−	14.3026i	0.702755	−	0.515430i
$771$	−1.73710	−	0.0949812i	−0.0625601	−	0.00342066i
$772$	−7.15788	+	10.9407i	−0.257618	+	0.393765i
$773$	−51.1521			−1.83981			−0.919907	−	0.392137i	$-0.871736\pi$
$773$	−51.1521			−1.83981			−0.919907	+	0.392137i	$0.871736\pi$
$774$	−28.8505	−	3.98108i	−1.03701	−	0.143097i
$775$	−0.350437			−0.0125881
$776$	−20.8053	+	9.79395i	−0.746868	+	0.351582i
$777$	38.5267	+	18.1906i	1.38214	+	0.652585i
$778$	11.7087	−	6.33160i	0.419777	−	0.226999i
$779$	19.3268	−	33.4751i	0.692456	−	1.19937i
$780$	−25.8439	−	19.0010i	−0.925359	−	0.680344i
$781$	7.51492	−	4.33874i	0.268905	−	0.155252i
$782$	−41.6822	+	67.7609i	−1.49055	+	2.42312i
$783$	−5.91330	−	15.7230i	−0.211324	−	0.561895i
$784$	9.88757	−	26.1961i	0.353128	−	0.935575i
$785$	−6.38863	−	11.0654i	−0.228020	−	0.394942i
$786$	−19.0969	−	1.57909i	−0.681164	−	0.0563241i
$787$	−28.5602	−	16.4892i	−1.01806	−	0.587778i	−0.104519	−	0.994523i	$-0.533330\pi$
$787$	−28.5602	−	16.4892i	−1.01806	−	0.587778i	−0.913542	+	0.406745i	$0.866664\pi$
$788$	1.07868	−	19.3273i	0.0384264	−	0.688506i
$789$	0.614072	−	0.940918i	0.0218615	−	0.0334976i
$790$	−0.875476	+	31.3971i	−0.0311480	+	1.11706i
$791$	6.03311	+	43.7301i	0.214513	+	1.55486i
$792$	−24.2323	−	4.73270i	−0.861057	−	0.168169i
$793$	−36.2888			−1.28865
$794$	19.3955	+	0.540824i	0.688322	+	0.0191931i
$795$	−9.34540	−	0.510989i	−0.331447	−	0.0181229i
$796$	−24.9059	−	1.39003i	−0.882767	−	0.0492684i
$797$	19.5546	−	33.8695i	0.692658	−	1.19972i	−0.278306	−	0.960493i	$-0.589773\pi$
$797$	19.5546	−	33.8695i	0.692658	−	1.19972i	0.970964	−	0.239227i	$-0.0768939\pi$
$798$	18.7004	+	9.47571i	0.661988	+	0.335437i
$799$	−12.7025	+	7.33379i	−0.449382	+	0.259451i
$800$	−0.140058	−	0.346413i	−0.00495179	−	0.0122476i
$801$	40.6116	+	29.7879i	1.43494	+	1.05250i
$802$	7.58453	−	12.3298i	0.267819	−	0.435381i
$803$	−9.66750	+	5.58153i	−0.341159	+	0.196968i
$804$	2.55977	−	23.0969i	0.0902761	−	0.814563i
$805$	−18.4280	+	45.2808i	−0.649502	+	1.59594i
$806$	14.8778	+	27.5128i	0.524050	+	0.969097i
$807$	15.3592	−	7.78216i	0.540670	−	0.273945i
$808$	8.94874	+	19.0099i	0.314816	+	0.668765i
$809$	−28.2736			−0.994049			−0.497024	−	0.867737i	$-0.665574\pi$
$809$	−28.2736			−0.994049			−0.497024	+	0.867737i	$0.665574\pi$
$810$	27.4182	+	6.89513i	0.963377	+	0.242270i
$811$			32.6884i			1.14784i	0.818910	+	0.573922i	$0.194579\pi$
$811$			32.6884i			1.14784i	−0.818910	+	0.573922i	$0.805421\pi$
$812$	7.32121	−	15.4606i	0.256924	−	0.542562i
$813$	22.6329	−	11.4676i	0.793770	−	0.402185i
$814$	33.6530	−	18.1982i	1.17954	−	0.637847i
$815$	14.0246	−	24.2914i	0.491261	−	0.850890i
$816$	16.3935	+	43.8898i	0.573888	+	1.53645i
$817$	19.2307	−	11.1028i	0.672797	−	0.388440i
$818$	−22.8508	−	14.0564i	−0.798958	−	0.491469i
$819$	−29.1051	−	15.7399i	−1.01702	−	0.549998i
$820$	47.3800	−	23.9391i	1.65458	−	0.835990i
$821$	−20.3558	+	11.7524i	−0.710421	+	0.410162i	−0.811217	−	0.584745i	$-0.801195\pi$
$821$	−20.3558	+	11.7524i	−0.710421	+	0.410162i	0.100796	+	0.994907i	$0.467861\pi$
$822$	−18.0224	−	12.4919i	−0.628605	−	0.435704i
$823$	4.97863	+	2.87441i	0.173544	+	0.100196i	0.584256	−	0.811570i	$-0.301386\pi$
$823$	4.97863	+	2.87441i	0.173544	+	0.100196i	−0.410712	+	0.911765i	$0.634720\pi$
$824$	2.94940	−	4.24495i	0.102747	−	0.147880i
$825$	0.0181752	−	0.332404i	0.000632779	−	0.0115728i
$826$	−5.06355	+	0.555251i	−0.176183	+	0.0193196i
$827$	−24.6927			−0.858651			−0.429325	−	0.903150i	$-0.641249\pi$
$827$	−24.6927			−0.858651			−0.429325	+	0.903150i	$0.641249\pi$
$828$	46.7364	−	17.5170i	1.62420	−	0.608756i
$829$	7.31685			0.254125			0.127062	−	0.991895i	$-0.459445\pi$
$829$	7.31685			0.254125			0.127062	+	0.991895i	$0.459445\pi$
$830$	0.623791	−	22.3710i	0.0216521	−	0.776507i
$831$	2.50915	−	3.84468i	0.0870416	−	0.133370i
$832$	−21.2507	+	25.7029i	−0.736735	+	0.891088i
$833$	−45.8724	−	11.6841i	−1.58938	−	0.404829i
$834$	5.13962	+	0.424985i	0.177971	+	0.0147160i
$835$	8.19922	+	14.2015i	0.283746	+	0.491462i
$836$	16.8023	−	8.48949i	0.581119	−	0.293615i
$837$	−21.3056	−	17.4938i	−0.736429	−	0.604676i
$838$	15.3365	+	9.43403i	0.529789	+	0.325893i
$839$	23.9776	+	41.5304i	0.827799	+	1.43379i	0.899761	+	0.436383i	$0.143741\pi$
$839$	23.9776	+	41.5304i	0.827799	+	1.43379i	−0.0719622	+	0.997407i	$0.522926\pi$
$840$	14.3665	+	24.9501i	0.495691	+	0.860860i
$841$	−9.27443	+	16.0638i	−0.319808	+	0.553924i
$842$	−2.14333	+	1.15903i	−0.0738640	+	0.0399428i
$843$	−30.2868	−	19.7661i	−1.04313	−	0.680781i
$844$	−6.55922	+	10.0257i	−0.225778	+	0.345098i
$845$	−9.72603			−0.334586
$846$	9.11582	+	1.25789i	0.313408	+	0.0432472i
$847$	0.916010	+	6.63957i	0.0314745	+	0.228138i
$848$	−1.08280	+	9.67037i	−0.0371837	+	0.332082i
$849$	−17.6066	−	0.962693i	−0.604256	−	0.0330395i
$850$	−0.555663	+	0.300481i	−0.0190591	+	0.0103064i
$851$	−38.6697	+	66.9780i	−1.32558	+	2.29597i
$852$	4.14839	+	9.46112i	0.142121	+	0.324133i
$853$	−10.6293	−	18.4105i	−0.363940	−	0.630363i	0.624665	−	0.780893i	$-0.285235\pi$
$853$	−10.6293	−	18.4105i	−0.363940	−	0.630363i	−0.988606	+	0.150530i	$0.951902\pi$
$854$	29.8143	+	13.1137i	1.02022	+	0.448742i
$855$	−19.7320	+	8.67842i	−0.674820	+	0.296796i
$856$	20.0016	+	1.67665i	0.683640	+	0.0573066i
$857$	11.5478	−	6.66710i	0.394464	−	0.227744i	−0.289629	−	0.957139i	$-0.593532\pi$
$857$	11.5478	−	6.66710i	0.394464	−	0.227744i	0.684092	+	0.729395i	$0.260198\pi$
$858$	−26.8686	+	12.6853i	−0.917279	+	0.433069i
$859$	13.7451	+	7.93572i	0.468976	+	0.270763i	0.715811	−	0.698294i	$-0.246057\pi$
$859$	13.7451	+	7.93572i	0.468976	+	0.270763i	−0.246835	+	0.969058i	$0.579391\pi$
$860$	30.4484	+	1.69936i	1.03828	+	0.0579478i
$861$	45.0052	−	31.1926i	1.53377	−	1.06304i
$862$	−1.14725	+	41.1436i	−0.0390754	+	1.40136i
$863$			11.5576i			0.393424i	0.980461	+	0.196712i	$0.0630264\pi$
$863$			11.5576i			0.393424i	−0.980461	+	0.196712i	$0.936974\pi$
$864$	8.77783	−	28.0526i	0.298628	−	0.954370i
$865$	−14.3785			−0.488885
$866$	1.07454	−	38.5363i	0.0365145	−	1.30952i
$867$	44.3899	−	22.4914i	1.50756	−	0.763847i
$868$	−2.28106	−	27.9805i	−0.0774242	−	0.949719i
$869$	25.1962	+	14.5470i	0.854722	+	0.493474i
$870$	7.50956	+	15.9059i	0.254598	+	0.539262i
$871$	−13.9827	−	24.2187i	−0.473786	−	0.820621i
$872$	−0.345455	+	4.12111i	−0.0116986	+	0.139558i
$873$	2.65927	−	24.2448i	0.0900025	−	0.820562i
$874$	−19.9389	+	32.4137i	−0.674442	+	1.09641i
$875$	−23.5074	+	18.2704i	−0.794694	+	0.617653i
$876$	−5.33666	−	12.1712i	−0.180309	−	0.411226i
$877$	−6.80279	−	3.92759i	−0.229714	−	0.132625i	0.380726	−	0.924688i	$-0.375674\pi$
$877$	−6.80279	−	3.92759i	−0.229714	−	0.132625i	−0.610440	+	0.792062i	$0.709007\pi$
$878$	7.75766	+	14.3458i	0.261808	+	0.484148i
$879$	1.57833	−	28.8659i	0.0532359	−	0.973624i
$880$	25.6927	+	2.87684i	0.866099	+	0.0969783i
$881$			1.84917i			0.0623000i	0.999515	+	0.0311500i	$0.00991696\pi$
$881$			1.84917i			0.0623000i	−0.999515	+	0.0311500i	$0.990083\pi$
$882$	18.2243	+	23.4494i	0.613645	+	0.789582i
$883$	−6.51703			−0.219315			−0.109658	−	0.993969i	$-0.534975\pi$
$883$	−6.51703			−0.219315			−0.109658	+	0.993969i	$0.534975\pi$
$884$	47.1815	+	30.8682i	1.58688	+	1.03821i
$885$	2.86262	−	4.38627i	0.0962258	−	0.147443i
$886$	−10.1283	−	18.7297i	−0.340267	−	0.629237i
$887$	17.2826	−	29.9344i	0.580293	−	1.00510i	−0.415151	−	0.909752i	$-0.636271\pi$
$887$	17.2826	−	29.9344i	0.580293	−	1.00510i	0.995444	−	0.0953448i	$-0.0303954\pi$
$888$	17.1201	+	42.2069i	0.574514	+	1.41637i
$889$	6.33072	+	8.14534i	0.212326	+	0.273186i
$890$	−44.9192	−	27.6315i	−1.50569	−	0.926209i
$891$	17.6986	−	19.3019i	0.592925	−	0.646638i
$892$	−18.5524	−	36.7186i	−0.621179	−	1.22943i
$893$	−6.07629	+	3.50815i	−0.203335	+	0.117396i
$894$	−16.5962	−	1.37231i	−0.555059	−	0.0458968i
$895$	−7.31290	+	12.6663i	−0.244443	+	0.423388i
$896$	26.7475	−	13.4377i	0.893571	−	0.448922i
$897$	32.8273	−	50.2999i	1.09607	−	1.67947i
$898$	−2.07327	−	0.0578109i	−0.0691859	−	0.00192918i
$899$		−	17.1513i		−	0.572027i
$900$	0.390938	+	0.0650970i	0.0130313	+	0.00216990i
$901$	16.4510			0.548061
$902$	1.37056	−	49.1521i	0.0456345	−	1.63659i
$903$	31.3504	−	2.59145i	1.04328	−	0.0862379i
$904$	−26.9276	+	38.7558i	−0.895600	+	1.28900i
$905$	23.7848	−	41.1964i	0.790632	−	1.36942i
$906$	−5.78786	+	8.35035i	−0.192289	+	0.277422i
$907$	−14.3959	−	24.9344i	−0.478008	−	0.827933i	0.521675	−	0.853145i	$-0.325307\pi$
$907$	−14.3959	−	24.9344i	−0.478008	−	0.827933i	−0.999682	+	0.0252112i	$0.991974\pi$
$908$	13.6605	−	6.90206i	0.453338	−	0.229053i
$909$	−22.1525	−	2.42978i	−0.734752	−	0.0805906i
$910$	31.7150	+	13.9497i	1.05134	+	0.462429i
$911$	9.16439	−	5.29106i	0.303630	−	0.175301i	−0.340443	−	0.940265i	$-0.610577\pi$
$911$	9.16439	−	5.29106i	0.303630	−	0.175301i	0.644072	+	0.764965i	$0.277244\pi$
$912$	7.84190	+	20.9949i	0.259671	+	0.695209i
$913$	−17.9527	−	10.3650i	−0.594147	−	0.343031i
$914$	−23.7327	−	43.8877i	−0.785009	−	1.45168i
$915$	−29.8747	+	15.1368i	−0.987627	+	0.500408i
$916$	6.14948	−	9.39938i	0.203184	−	0.310564i
$917$	20.5032	−	2.82867i	0.677075	−	0.0934108i
$918$	−48.7828	−	9.47034i	−1.61007	−	0.312568i
$919$		−	1.15863i		−	0.0382198i	−0.999817	−	0.0191099i	$-0.993917\pi$
$919$		−	1.15863i		−	0.0382198i	0.999817	−	0.0191099i	$-0.00608324\pi$
$920$	−47.2853	+	22.2592i	−1.55895	+	0.733863i
$921$	21.2887	+	42.0162i	0.701485	+	1.38448i
$922$	−10.9230	−	20.1993i	−0.359730	−	0.665229i
$923$	10.7665	+	6.21604i	0.354384	+	0.204604i
$924$	26.6589	−	0.712487i	0.877013	−	0.0234391i
$925$	−0.531839	+	0.307057i	−0.0174868	+	0.0100960i
$926$	14.1045	+	8.67621i	0.463503	+	0.285118i
$927$	2.20725	+	5.01860i	0.0724958	+	0.164833i
$928$	16.9543	−	6.85477i	0.556552	−	0.225019i
$929$	9.15603	−	5.28624i	0.300400	−	0.173436i	−0.342223	−	0.939619i	$-0.611180\pi$
$929$	9.15603	−	5.28624i	0.300400	−	0.173436i	0.642622	+	0.766183i	$0.277846\pi$
$930$	23.7243	+	16.4440i	0.777951	+	0.539220i
$931$	−21.9432	−	5.58912i	−0.719160	−	0.183176i
$932$	−22.2306	−	1.24072i	−0.728188	−	0.0406411i
$933$	1.20038	−	21.9537i	0.0392988	−	0.718730i
$934$	−0.513238	+	18.4062i	−0.0167937	+	0.602270i
$935$		−	43.7077i		−	1.42939i
$936$	−11.4866	−	33.4562i	−0.375450	−	1.09355i
$937$		−	37.9228i		−	1.23888i	−0.785042	−	0.619442i	$-0.787359\pi$
$937$		−	37.9228i		−	1.23888i	0.785042	−	0.619442i	$-0.212641\pi$
$938$	2.73600	+	24.9506i	0.0893336	+	0.814667i
$939$	6.31934	−	9.68287i	0.206224	−	0.315989i
$940$	−9.62071	−	0.536945i	−0.313793	−	0.0175132i
$941$	−5.07267	+	8.78612i	−0.165364	+	0.286419i	−0.936785	−	0.349907i	$-0.886213\pi$
$941$	−5.07267	+	8.78612i	−0.165364	+	0.286419i	0.771420	+	0.636326i	$0.219547\pi$
$942$	1.16113	−	14.0422i	0.0378315	−	0.457521i
$943$	49.7000	+	86.0829i	1.61845	+	2.80325i
$944$	−4.38376	−	3.23067i	−0.142679	−	0.105149i
$945$	−30.5262	−	0.817508i	−0.993017	−	0.0265936i
$946$	14.8003	−	24.0601i	0.481199	−	0.782262i
$947$	19.1797	+	33.2203i	0.623257	+	1.07951i	0.988875	+	0.148748i	$0.0475244\pi$
$947$	19.1797	+	33.2203i	0.623257	+	1.07951i	−0.365618	+	0.930765i	$0.619142\pi$
$948$	−20.5172	+	27.9061i	−0.666367	+	0.906348i
$949$	−13.8505	−	7.99658i	−0.449605	−	0.259580i
$950$	−0.265804	+	0.143736i	−0.00862381	+	0.00466342i
$951$	−27.0795	+	41.4929i	−0.878114	+	1.34550i
$952$	−27.6086	−	42.4107i	−0.894801	−	1.37454i
$953$	−18.6032			−0.602616			−0.301308	−	0.953527i	$-0.597423\pi$
$953$	−18.6032			−0.602616			−0.301308	+	0.953527i	$0.597423\pi$
$954$	−8.14899	−	6.33391i	−0.263833	−	0.205068i
$955$			9.23150i			0.298724i
$956$	0.185908	+	0.121629i	0.00601268	+	0.00393376i
$957$	16.2686	+	0.889538i	0.525891	+	0.0287547i
$958$	13.7823	+	25.4869i	0.445287	+	0.823445i
$959$	21.9382	+	8.92822i	0.708421	+	0.288307i
$960$	−6.77337	+	30.0240i	−0.218609	+	0.969020i
$961$	1.42661	+	2.47097i	0.0460198	+	0.0797086i
$962$	46.6863	+	28.7185i	1.50523	+	0.925921i
$963$	−12.5914	+	17.1666i	−0.405752	+	0.553185i
$964$	−43.3910	+	21.9237i	−1.39753	+	0.706114i
$965$	7.26026	+	12.5751i	0.233716	+	0.404808i
$966$	−45.1473	+	29.4627i	−1.45259	+	0.947948i
$967$	46.2821	+	26.7210i	1.48833	+	0.859290i	0.999911	−	0.0133176i	$-0.00423926\pi$
$967$	46.2821	+	26.7210i	1.48833	+	0.859290i	0.488422	+	0.872607i	$0.337573\pi$
$968$	−4.08844	+	5.88432i	−0.131407	+	0.189129i
$969$	33.7984	−	17.1249i	1.08576	−	0.550131i
$970$	−0.711855	+	25.5292i	−0.0228563	+	0.819694i
$971$		−	29.5647i		−	0.948777i	−0.880316	−	0.474388i	$-0.842669\pi$
$971$		−	29.5647i		−	0.948777i	0.880316	−	0.474388i	$-0.157331\pi$
$972$	20.5183	+	23.4734i	0.658125	+	0.752909i
$973$	−5.51810	+	0.761290i	−0.176902	+	0.0244058i
$974$	−1.38705	+	49.7437i	−0.0444440	+	1.59389i
$975$	0.425446	−	0.215564i	0.0136252	−	0.00690357i
$976$	13.9462	+	31.9048i	0.446408	+	1.02125i
$977$	22.7035	−	39.3236i	0.726350	−	1.25807i	−0.232066	−	0.972700i	$-0.574549\pi$
$977$	22.7035	−	39.3236i	0.726350	−	1.25807i	0.958416	−	0.285375i	$-0.0921180\pi$
$978$	27.9708	−	13.2056i	0.894406	−	0.422270i
$979$	−42.3052	+	24.4249i	−1.35208	+	0.780625i
$980$	−21.0154	−	22.9217i	−0.671314	−	0.732207i
$981$	−3.53699	−	2.59432i	−0.112927	−	0.0828302i
$982$	−9.75290	+	15.8548i	−0.311228	+	0.505948i
$983$	−16.2920	−	28.2185i	−0.519633	−	0.900030i	−0.999740	−	0.0228201i	$-0.992736\pi$
$983$	−16.2920	−	28.2185i	−0.519633	−	0.900030i	0.480107	−	0.877210i	$-0.340598\pi$
$984$	57.9803	+	8.06747i	1.84834	+	0.257181i
$985$	−18.6185	−	10.7494i	−0.593234	−	0.342504i
$986$	−14.7063	−	27.1955i	−0.468343	−	0.866082i
$987$	−9.90573	+	0.818814i	−0.315303	+	0.0260631i
$988$	22.5694	+	14.7659i	0.718029	+	0.469766i
$989$			57.1031i			1.81577i
$990$	−16.8282	+	21.6506i	−0.534836	+	0.688101i
$991$		−	14.1154i		−	0.448390i	−0.974544	−	0.224195i	$-0.928025\pi$
$991$		−	14.1154i		−	0.448390i	0.974544	−	0.224195i	$-0.0719752\pi$
$992$	18.4713	−	23.6540i	0.586463	−	0.751014i
$993$	−13.1218	−	8.56370i	−0.416408	−	0.271761i
$994$	−6.59928	−	8.99769i	−0.209316	−	0.285390i
$995$	−13.8521	+	23.9925i	−0.439141	+	0.760614i
$996$	14.6188	−	19.8835i	0.463215	−	0.630034i
$997$	4.86865	+	8.43275i	0.154192	+	0.267068i	0.932764	−	0.360487i	$-0.117389\pi$
$997$	4.86865	+	8.43275i	0.154192	+	0.267068i	−0.778573	+	0.627554i	$0.784056\pi$
$998$	−10.4851	+	17.0452i	−0.331901	+	0.539556i
$999$	−47.6626	−	7.88120i	−1.50798	−	0.249350i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.be.a.139.3	✓	184
7.6	odd	2	inner	504.2.be.a.139.4	yes	184
8.3	odd	2	inner	504.2.be.a.139.61	yes	184
9.7	even	3	inner	504.2.be.a.475.62	yes	184
56.27	even	2	inner	504.2.be.a.139.62	yes	184
63.34	odd	6	inner	504.2.be.a.475.61	yes	184
72.43	odd	6	inner	504.2.be.a.475.4	yes	184
504.475	even	6	inner	504.2.be.a.475.3	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.be.a.139.3	✓	184	1.1	even	1	trivial
504.2.be.a.139.4	yes	184	7.6	odd	2	inner
504.2.be.a.139.61	yes	184	8.3	odd	2	inner
504.2.be.a.139.62	yes	184	56.27	even	2	inner
504.2.be.a.475.3	yes	184	504.475	even	6	inner
504.2.be.a.475.4	yes	184	72.43	odd	6	inner
504.2.be.a.475.61	yes	184	63.34	odd	6	inner
504.2.be.a.475.62	yes	184	9.7	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41366 - 0.0394185i) q^{2} +(-1.54504 + 0.782839i) q^{3} +(1.99689 + 0.111449i) q^{4} +(1.11062 - 1.92366i) q^{5} +(2.21503 - 1.04577i) q^{6} +(-2.08899 + 1.62361i) q^{7} +(-2.81854 - 0.236266i) q^{8} +(1.77433 - 2.41904i) q^{9} +O(q^{10})\)	\(q+(-1.41366 - 0.0394185i) q^{2} +(-1.54504 + 0.782839i) q^{3} +(1.99689 + 0.111449i) q^{4} +(1.11062 - 1.92366i) q^{5} +(2.21503 - 1.04577i) q^{6} +(-2.08899 + 1.62361i) q^{7} +(-2.81854 - 0.236266i) q^{8} +(1.77433 - 2.41904i) q^{9} +(-1.64588 + 2.67563i) q^{10} +(1.45488 + 2.51993i) q^{11} +(-3.17253 + 1.39105i) q^{12} +(-2.08438 + 3.61026i) q^{13} +(3.01714 - 2.21289i) q^{14} +(-0.210050 + 3.84158i) q^{15} +(3.97516 + 0.445104i) q^{16} -6.76243i q^{17} +(-2.60366 + 3.34977i) q^{18} -3.23484i q^{19} +(2.43219 - 3.71756i) q^{20} +(1.95657 - 4.14389i) q^{21} +(-1.95738 - 3.61968i) q^{22} +(7.20408 + 4.15928i) q^{23} +(4.53973 - 1.84142i) q^{24} +(0.0330268 + 0.0572040i) q^{25} +(3.08893 - 5.02153i) q^{26} +(-0.847693 + 5.12654i) q^{27} +(-4.35245 + 3.00935i) q^{28} +(-2.79971 + 1.61641i) q^{29} +(0.448370 - 5.42242i) q^{30} +(-2.65268 + 4.59457i) q^{31} +(-5.60199 - 0.785922i) q^{32} +(-4.22055 - 2.75446i) q^{33} +(-0.266565 + 9.55981i) q^{34} +(0.803179 + 5.82173i) q^{35} +(3.81274 - 4.63282i) q^{36} +9.29723i q^{37} +(-0.127512 + 4.57297i) q^{38} +(0.394215 - 7.20975i) q^{39} +(-3.58484 + 5.15951i) q^{40} +(10.3483 + 5.97460i) q^{41} +(-2.92927 + 5.78095i) q^{42} +(3.43228 + 5.94488i) q^{43} +(2.62440 + 5.19417i) q^{44} +(-2.68280 - 6.09984i) q^{45} +(-10.0202 - 6.16379i) q^{46} +(-1.08449 - 1.87839i) q^{47} +(-6.49024 + 2.42420i) q^{48} +(1.72779 - 6.78342i) q^{49} +(-0.0444338 - 0.0821691i) q^{50} +(5.29390 + 10.4483i) q^{51} +(-4.56465 + 6.97700i) q^{52} +2.43270i q^{53} +(1.40043 - 7.21379i) q^{54} +6.46330 q^{55} +(6.27152 - 4.08265i) q^{56} +(2.53236 + 4.99797i) q^{57} +(4.02156 - 2.17470i) q^{58} +(-1.17901 - 0.680701i) q^{59} +(-0.847588 + 7.64781i) q^{60} +(4.35247 + 7.53869i) q^{61} +(3.93111 - 6.39062i) q^{62} +(0.221020 + 7.93418i) q^{63} +(7.88836 + 1.33185i) q^{64} +(4.62994 + 8.01928i) q^{65} +(5.85787 + 4.06025i) q^{66} +(-3.35416 + 5.80957i) q^{67} +(0.753668 - 13.5039i) q^{68} +(-14.3867 - 0.786635i) q^{69} +(-0.905941 - 8.26163i) q^{70} -2.98220i q^{71} +(-5.57255 + 6.39896i) q^{72} +3.83642i q^{73} +(0.366483 - 13.1432i) q^{74} +(-0.0958094 - 0.0625281i) q^{75} +(0.360520 - 6.45962i) q^{76} +(-7.13061 - 2.90196i) q^{77} +(-0.841486 + 10.1766i) q^{78} +(8.65919 - 4.99939i) q^{79} +(5.27114 - 7.15250i) q^{80} +(-2.70353 - 8.58434i) q^{81} +(-14.3935 - 8.85399i) q^{82} +(-6.16981 + 3.56214i) q^{83} +(4.36888 - 8.05685i) q^{84} +(-13.0086 - 7.51052i) q^{85} +(-4.61775 - 8.53935i) q^{86} +(3.06028 - 4.68915i) q^{87} +(-3.50527 - 7.44626i) q^{88} +16.7883i q^{89} +(3.55213 + 8.72888i) q^{90} +(-1.50738 - 10.9260i) q^{91} +(13.9222 + 9.10851i) q^{92} +(0.501695 - 9.17544i) q^{93} +(1.45906 + 2.69816i) q^{94} +(-6.22272 - 3.59269i) q^{95} +(9.27058 - 3.17117i) q^{96} +(7.04084 - 4.06503i) q^{97} +(-2.70991 + 9.52136i) q^{98} +(8.67724 + 0.951755i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q - 2 q^{2} - 2 q^{4} - 8 q^{8} - 8 q^{9}+O(q^{10}) \) 184 * q - 2 * q^2 - 2 * q^4 - 8 * q^8 - 8 * q^9	\( 184 q - 2 q^{2} - 2 q^{4} - 8 q^{8} - 8 q^{9} - 4 q^{11} - 10 q^{14} - 2 q^{16} - 10 q^{18} + 6 q^{22} - 80 q^{25} - 12 q^{28} + 4 q^{30} - 12 q^{32} + 12 q^{35} - 46 q^{36} + 10 q^{42} - 4 q^{43} - 36 q^{44} - 16 q^{46} - 2 q^{49} + 16 q^{50} - 24 q^{51} + 40 q^{56} + 16 q^{57} - 10 q^{58} + 40 q^{60} - 8 q^{64} + 36 q^{65} - 4 q^{67} - 76 q^{72} - 40 q^{74} + 60 q^{78} + 8 q^{81} + 40 q^{84} + 32 q^{86} - 18 q^{88} + 20 q^{91} - 26 q^{92} - 132 q^{98} + 28 q^{99}+O(q^{100}) \) 184 * q - 2 * q^2 - 2 * q^4 - 8 * q^8 - 8 * q^9 - 4 * q^11 - 10 * q^14 - 2 * q^16 - 10 * q^18 + 6 * q^22 - 80 * q^25 - 12 * q^28 + 4 * q^30 - 12 * q^32 + 12 * q^35 - 46 * q^36 + 10 * q^42 - 4 * q^43 - 36 * q^44 - 16 * q^46 - 2 * q^49 + 16 * q^50 - 24 * q^51 + 40 * q^56 + 16 * q^57 - 10 * q^58 + 40 * q^60 - 8 * q^64 + 36 * q^65 - 4 * q^67 - 76 * q^72 - 40 * q^74 + 60 * q^78 + 8 * q^81 + 40 * q^84 + 32 * q^86 - 18 * q^88 + 20 * q^91 - 26 * q^92 - 132 * q^98 + 28 * q^99

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